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In this article, we generalize, improve, unify and enrich some results for Jaggi- W -contraction-type mappings in the framework of b-metric-like spaces. Our results supplement numerous methods in the existing literature, and we created new approach to prove that a Picard sequence is Cauchy in a b-metric-like space. Among other things, we prove Wardowski's theorem, but now by using only the property (W 1). Our proofs in this article are much shorter than ones in recently published papers. [ABSTRACT FROM AUTHOR]

Very recently, Proinov introduced a great family of contractions in the setting of complete metric spaces that has attracted the attention of many researchers because of the very weak conditions that are assumed on the involved functions. Inspired by Proinov's results, in this paper, we introduce a new class of contractions in the setting of fuzzy metric spaces (in the sense of George and Veeramani) that are able to translate to this framework the best advantages of the abovementioned auxiliary functions. Accordingly, we present some results about the existence and uniqueness of fixed points for this class of fuzzy contractions in the setting of non-Archimedean fuzzy metric spaces. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new contraction-type mapping and provide a fixed-point theorem which generalizes and improves some existing results in the literature. Thus, we prove that the Boyd and Wong theorem (1969) and, more recently, the fixed-point results due to Wardowski (2012), Turinici (2012), Piri and Kumam (2016), Secelean (2016), Proinov (2020), and others are consequences of our main result. An application in integral equations and some illustrative examples are indicated. [ABSTRACT FROM AUTHOR]

In the present paper, the concept of almost periodic waves is introduced to discontinuous impulsive fractional inclusions involving Caputo fractional derivative. New results on the existence and uniqueness are established by using the theory of operator semigroups, Hausdorff measure of noncompactness, fixed point theorems and fractional calculus techniques. Applications to a class of fractional-order impulsive gene regulatory network (GRN) models are proposed to illustrate the results. [ABSTRACT FROM AUTHOR]

The main intention of the present research study is focused on the analysis of a Caputo fractional integro-differential boundary problem (CFBVP) in which the right-hand side of supposed differential equation is represented as a sum of two nonlinear terms. Under the integro-derivative boundary conditions, we extract an equivalent integral equation and then define new operators based on it. With the help of three distinct fixed-point theorems attributed to Krasnosel'skiĭ, Leray–Schauder, and Banach, we investigate desired uniqueness and existence results. Additionally, the dependence criterion of solutions for this CFBVP is checked via the generalized version of the Gronwall inequality. Next, three simulative examples are designed to examine our findings based on the procedures applied in the theorems. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to introduce and study some fixed point results for rational multivalued G-contraction and F-Khan-type multivalued contraction mappings on a metric space with a graph. At the end, we give an illustrative example. [ABSTRACT FROM AUTHOR]

The present paper aims to introduce the concept of weak-fuzzy contraction mappings in the graph structure within the context of fuzzy cone metric spaces. We prove some fixed point results endowed with a graph using weak-fuzzy contractions. By relaxing the continuity condition of mappings involved, our results enrich and generalize some well-known results in fixed point theory. With the help of new lemmas, our proofs are straight forward. We furnish the validity of our findings with appropriate examples. This approach is completely new and will be beneficial for the future aspects of the related study. We provide an application of integral equations to illustrate the usability of our theory. [ABSTRACT FROM AUTHOR]

The terms of F − integral contraction as well as (ϖ , ζ ˜ , F , i) − integral contraction are introduced. Fixed point and common fixed point theorems are established. For the mapping F we use only the supposition that it is strictly increasing. As a consequence of the main theorems we obtain Jungck–Wardowski, Branciari–Wardowski and Jungck–Branciari type results. Consequently, the results presented in the article enhance and complement some known results in literature. [ABSTRACT FROM AUTHOR]

In the present paper, we introduce a new type of quartic functional equation and examine the Hyers–Ulam stability in fuzzy normed spaces by employing the direct method and fixed point techniques. We provide some applications in which the stability of this quartic functional equation can be controlled by sums and products of powers of norms. In particular, we show that if the control function is the fuzzy norm of the product of powers of norms, the quartic functional equation is hyperstable. [ABSTRACT FROM AUTHOR]

One of the main goals of this paper is to obtain new contractive conditions using the method of a strictly increasing mapping F : (0 , + ∞) → (− ∞ , + ∞) . According to the recently obtained results, this was possible (Wardowski's method) only if two more properties (F 2) and (F 3) were used instead of the aforementioned strictly increasing (F 1) . Using only the fact that the function F is strictly increasing, we came to new families of contractive conditions that have not been found in the existing literature so far. Assuming that α (u , v) = 1 for every u and v from metric space Ξ , we obtain some contractive conditions that can be found in the research of Rhoades (Trans. Amer. Math. Soc. 1977, 222) and Collaco and Silva (Nonlinear Anal. TMA 1997). Results of the paper significantly improve, complement, unify, generalize and enrich several results known in the current literature. In addition, we give examples with results in line with the ones we obtained. [ABSTRACT FROM AUTHOR]

Using some of the extended fixed point results for Geraghty contractions in b-metric spaces given by Faraji, Savić and Radenović and their idea to apply these results to nonlinear integral equations, in this paper we present some existence and uniqueness conditions for the solution of a nonlinear Fredholm–Volterra integral equation with a modified argument. [ABSTRACT FROM AUTHOR]

In this paper, we give an affirmative answer to an open question posed recently by Mlaiki et al. As a consequence of our results, we get some known results in the literature. We also give an application of our results to the existence of a solution of nonlinear fractional differential equations. [ABSTRACT FROM AUTHOR]

We introduce a new projection and contraction method with inertial and self-adaptive techniques for solving variational inequalities and split common fixed point problems in real Hilbert spaces. The stepsize of the algorithm is selected via a self-adaptive method and does not require prior estimate of norm of the bounded linear operator. More so, the cost operator of the variational inequalities does not necessarily needs to satisfies Lipschitz condition. We prove a strong convergence result under some mild conditions and provide an application of our result to split common null point problems. Some numerical experiments are reported to illustrate the performance of the algorithm and compare with some existing methods. [ABSTRACT FROM AUTHOR]

We propose a notion of w-distance for fuzzy metric spaces, in the sense of Kramosil and Michalek, which allows us to obtain a characterization of complete fuzzy metric spaces via a suitable fixed point theorem that is proved here. Our main result provides a fuzzy counterpart of a renowned characterization of complete metric spaces due to Suzuki and Takahashi. [ABSTRACT FROM AUTHOR]

In this study, we introduce set-valued Prešić type almost contractive mapping, Prešić type almost F-contractive mapping and set-valued Prešić type almost F-contractive mapping in metric space and prove some fixed point results for these mappings. Additionally, we give examples to show that our main theorems are applicable. These examples show that the new class of set-valued Prešić type almost F-contractive operators is not included in Prešić type class of set-valued Prešić type almost contractive operators. [ABSTRACT FROM AUTHOR]

In this paper we present an algorithm which counts the number of fixed point orbits of an AND-OR dynamical system. We further extend the algorithm in order to list all its fixed point orbits (FPOs) in polynomial time on the number of FPOs of the system. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of d * -complete topological spaces, which include earlier defined classes of complete metric spaces and quasi b-metric spaces. Further, we prove some fixed point results for mappings defined on d * -complete topological spaces, generalizing earlier results of Tasković, Ćirić and Prešić, Prešić, Bryant, Marjanović, Yen, Caccioppoli, Reich and Bianchini. [ABSTRACT FROM AUTHOR]

In this paper we consider a kind of Geraghty contractions by using m w -distances in the setting of complete quasi-metric spaces. We provide fixed point theorems for this type of mappings and illustrate with some examples the results obtained. [ABSTRACT FROM AUTHOR]

In the present work, we study many fixed point results in intuitionistic generalized fuzzy cone metric space. Precisely, we prove new common fixed point theorems for three self mappings that do not require any commutativity or continuity but a generalized contractive condition. Our results are generalizations for many results in the literature. Some examples are given to support these results. [ABSTRACT FROM AUTHOR]

In this paper, we enlarge the class of C * -algebra valued partial metric spaces as well as the class of C * -algebra valued b-metric spaces by introducing the class of C * -algebra valued partial b-metric spaces and utilize the same to prove our fixed point results. We furnish an example to highlight the utility of our main result. Finally, we apply our result in order to examine the existence and uniqueness of a solution for the system of Fredholm integral equations. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to introduce the ( α , β )-type ϑ -contraction, ( α , β )-type rational ϑ -contraction, and cyclic ( α - ϑ ) contraction. Based on these definitions we prove fixed point theorems in the complete metric spaces. These results extend and improve some known results in the literature. As an application of the proved fixed point Theorems, we study the existence of solutions of an integral boundary value problem for scalar nonlinear Caputo fractional differential equations with a fractional order in (1,2). [ABSTRACT FROM AUTHOR]

In our recent work we have introduced and studied a notion of a generalized nonexpansive mapping. In the definition of this notion the norm has been replaced by a general function satisfying certain conditions. For this new class of mappings, we have established the existence of unique fixed points and the convergence of iterates. In the present paper we construct an example of a generalized nonexpansive self-mapping of a bounded, closed and convex set in a Hilbert space, which is not nonexpansive in the classical sense. [ABSTRACT FROM AUTHOR]

We present a condition that guarantees the existence and uniqueness of fixed (or best proximity) points in complete metric space (or uniformly convex Banach spaces) for a wide class of cyclic maps, called p–cyclic summing maps. These results generalize some known results from fixed point theory. We find a priori and a posteriori error estimates of the fixed (or best proximity) point for the Picard iteration associated with the investigated class of maps, provided that the modulus of convexity of the underlying space is of power type. We illustrate the results with some applications and examples. [ABSTRACT FROM AUTHOR]

In this current work, we introduce the finite variable additive functional equation and we derive its solution. In fact, we investigate the Hyers–Ulam stability results for the finite variable additive functional equation in fuzzy normed space by two different approaches of direct and fixed point methods. [ABSTRACT FROM AUTHOR]

Nowadays, demicontractive operators in terms of admissible perturbation are used to solve difficult tasks. The current research uses several demicontractive operators in order to enhance the quality of the edge detection results when using ant-based algorithms. Two new operators are introduced, χ -operator and K H -operator, the latter one is a Krasnoselskij admissible perturbation of a demicontractive operator. In order to test the efficiency of the new operators, a comparison is made with a trigonometric operator. Ant Colony Optimization (ACO) is the solver chosen for the images edge detection problem. Demicontractive operators in terms of admissible perturbation are used during the construction phase of the matrix of ants artificial pheromone, namely the edge information of an image. The conclusions of statistical analysis on the results shows a positive influence of proposed operators for image edge detection of medical images. [ABSTRACT FROM AUTHOR]

In this paper we present some novel fixed point theorems for a family of contractions depending on two functions (that are not defined on t = 0 ) and on some parameters that we have called multiparametric contractions. We develop our study in the setting of b-metric spaces because they allow to consider some families of functions endowed with b-metrics deriving from similarity measures that are more general than norms. Taking into account that the contractivity condition we will employ is very general (of Hardy-Rogers type), we will discuss the validation and usage of this novel condition. After that, we introduce the main results of this paper and, finally, we deduce some consequences of them which illustrates the wide applicability of the main results. [ABSTRACT FROM AUTHOR]

The purpose of this manuscript is to provide much simpler and shorter proofs of some recent significant results in the context of generalized F-Suzuki-contraction mappings in b-complete b-metric spaces. By using our new approach for the proof that a Picard sequence is b-Cauchy, our results generalize, complement and improve many known results in the existing literature. Further, some new contractive conditions are provided here to illustrate the usability of the obtained theoretical results. [ABSTRACT FROM AUTHOR]

The concepts of b-metric spaces and ω t -distance mappings play a key role in solving various kinds of equations through fixed point theory in mathematics and other science. In this article, we study some fixed point results through these concepts. We introduce a new kind of function namely, H -simulation function which is used in this manuscript together with the notion of ω t -distance mappings to furnish for new contractions. Many fixed point results are proved based on these new contractions as well as some examples are introduced. Moreover, we introduce an application on matrix equations to focus on the importance of our work. [ABSTRACT FROM AUTHOR]

In this manuscript we discuss, consider, generalize, improve and unify several recent results for so-called F-contraction-type mappings in the framework of complete metric spaces. We also introduce (φ , F) -weak contraction and establish the corresponding fixed point result. Using our new approach for the proof that a Picard sequence is a Cauchy in metric space, our obtained results complement and enrich several methods in the existing literature. At the end we give one open question for F-contraction of Ćirić-type mapping. [ABSTRACT FROM AUTHOR]

The aim of this article is to introduce a new class of contraction-like mappings, called the almost multivalued ( Θ , δ b )-contraction mappings in the setting of b-metric spaces to obtain some generalized fixed point theorems. As an application of our main result, we present the sufficient conditions for the existence of solutions of Fredholm integral inclusions. An example is also provided to verify the effectiveness and applicability of our main results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce some common fixed point theorems for two distinct self-mappings in the setting of metric spaces by using the notion of a simulation function introduced in 2015. The contractivity conditions have not to be verified for all pairs of points of the space because it is endowed with an antecedent conditions. They are also of rational type because the involved terms in the contractivity upper bound are expressed, in some cases, as quotients. [ABSTRACT FROM AUTHOR]

In this article, we introduce a relatively new concept of multi-valued (θ , R) -contractions and utilize the same to prove some fixed point results for a special class of multi-valued mappings in metric spaces endowed with an amorphous binary relation. Illustrative examples are also provided to exhibit the utility of our results proved herein. Finally, we utilize some of our results to investigate the existence and uniqueness of a positive solution for the integral equation of Volterra type. [ABSTRACT FROM AUTHOR]

Starting from two extensions of the Banach contraction principle due to Ćirić (1974) and Wardowski (2012), in the present paper we introduce the concepts of Ćirić type ψ F -contraction and ψ F -quasicontraction on a metric space and give some sufficient conditions under which the respective mappings are Picard operators. Some known fixed point results from the literature can be obtained as particular cases. [ABSTRACT FROM AUTHOR]

In this paper, by using admissible mapping, Wong type contraction mappings are extended and investigated in the framework of quasi-metric spaces to guarantee the existence of fixed points. We consider examples to illustrate the main results. We also demonstrate that the main results of the paper cover several existing results in the literature. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to define generalized ( α β - ψ) -contraction in the context of F -metric space and obtain some new fixed point results. As applications, we solve a nonlinear neutral differential equation with an unbounded delay ϑ / (ι) = − ρ 1 (ι) ϑ (ι) + ρ 2 (ι) L (ϑ (ι − ς (ι))) + ρ 3 (ι) ϑ / (ι − ς (ι)) , where ρ 1 (ι) , ρ 2 (ι) are continuous, ρ 3 (ι) is continuously differentiable and ς (ι) > 0 , for all ι ∈ R and is twice continuously differentiable. [ABSTRACT FROM AUTHOR]

Kannan maps have inspired a branch of metric fixed point theory devoted to the extension of the classical Banach contraction principle. The study of these maps in modular vector spaces was attempted timidly and was not successful. In this work, we look at this problem in the variable exponent sequence spaces lp(·). We prove the modular version of most of the known facts about these maps in metric and Banach spaces. In particular, our results for Kannan nonexpansive maps in the modular sense were never attempted before. [ABSTRACT FROM AUTHOR]

In this paper, an extension of Darbo's fixed point theorem via θ -F-contractions in a Banach space has been presented. Measure of noncompactness approach is the main tool in the presentation of our proofs. As an application, we study the existence of solutions for a system of integral equations. Finally, we present a concrete example to support the effectiveness of our results. [ABSTRACT FROM AUTHOR]

The projected subgradient algorithms can be considered as an improvement of the projected algorithms and the subgradient algorithms for the equilibrium problems of the class of monotone and Lipschitz continuous operators. In this paper, we present and analyze an iterative algorithm for finding a common element of the fixed point of pseudocontractive operators and the pseudomonotone equilibrium problem in Hilbert spaces. The suggested iterative algorithm is based on the projected method and subgradient method with a linearsearch technique. We show the strong convergence result for the iterative sequence generated by this algorithm. Some applications are also included. Our result improves and extends some existing results in the literature. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to present some new fixed point results in the generalized metric spaces of Perov's sense under a contractive condition of Hardy–Rogers type. The data dependence of the fixed point set, the well-posedness of the fixed point problem and the Ulam–Hyers stability are also studied. [ABSTRACT FROM AUTHOR]

In this paper, using a new shrinking projection method, we deal with the strong convergence for finding a common point of the sets of zero points of a maximal monotone mapping, common fixed points of a finite family of demimetric mappings and common zero points of a finite family of inverse strongly monotone mappings in a Hilbert space. Using this result, we get well-known and new strong convergence theorems in a Hilbert space. [ABSTRACT FROM AUTHOR]

In this manuscript, we define a new contraction mapping, Pata-Ćirić type contraction at a point, that merges distinct contractions defined by Seghal, Pata and Ćirić. We proved that in a complete space, each Pata-Ćirić type contraction at a point possesses a fixed point. We express an example to illustrate the observed result. [ABSTRACT FROM AUTHOR]

The aim of the present paper is to state and prove some convergence theorems for the Mann and Ishikawa iteration schemes involving C * -algebra-multi-valued contractive mappings in the setting of convex C * -algebra-valued metric spaces. The convergence theorems of the proposed iterations to a common fixed point of finite and infinite family of such mappings are also established. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notions of α -almost Istrăt̨escu contraction of type E and of type E ∗ in the setting of b-metric space. The existence of fixed points for such mappings is investigated and some examples to illustrate the validity of the main results are considered. In the last part of the paper, we list some immediate consequences. [ABSTRACT FROM AUTHOR]

In this work, we investigate the modular version of the Ekeland variational principle (EVP) in the context of variable exponent sequence spaces ℓ p (·) . The core obstacle in the development of a modular version of the EVP is the failure of the triangle inequality for the module. It is the lack of this inequality, which is indispensable in the establishment of the classical EVP, that has hitherto prevented a successful treatment of the modular case. As an application, we establish a modular version of Caristi's fixed point theorem in ℓ p (·) . [ABSTRACT FROM AUTHOR]

In this paper, we study the existence of solutions for a new nonlocal boundary value problem of integro-differential equations involving mixed left and right Caputo and Riemann–Liouville fractional derivatives and Riemann–Liouville fractional integrals of different orders. Our results rely on the standard tools of functional analysis. Examples are constructed to demonstrate the application of the derived results. [ABSTRACT FROM AUTHOR]

The main aim of the current paper is the investigation of possibilities for improvements and generalizations contractive condition of Ćirić in the fuzzy metric spaces. Various versions of fuzzy contractive conditions are studied in two directions. First, motivated by recent results, more general contractive conditions in fuzzy metric spaces are achieved and secondly, quasi-contractive type of mappings are investigated in order to obtain fixed point results with a wider class of t-norms. [ABSTRACT FROM AUTHOR]

In recent works, many authors generated strongly relatively nonexpansive sequences of mappings by the sequences of firmly nonexpansive-like mappings. In this paper, we introduce a new method for construction of strongly relatively nonexpansive sequences from firmly nonexpansive-like mappings. [ABSTRACT FROM AUTHOR]

With the help of C-contractions having a fixed point, we obtain a characterization of complete fuzzy metric spaces, in the sense of Kramosil and Michalek, that extends the classical theorem of H. Hu (see "Am. Math. Month. 1967, 74, 436–437") that a metric space is complete if and only if any Banach contraction on any of its closed subsets has a fixed point. We apply our main result to deduce that a well-known fixed point theorem due to D. Mihet (see "Fixed Point Theory 2005, 6, 71–78") also allows us to characterize the fuzzy metric completeness. [ABSTRACT FROM AUTHOR]

In this paper, we study a class of Caputo fractional q-difference inclusions in Banach spaces. We obtain some existence results by using the set-valued analysis, the measure of noncompactness, and the fixed point theory (Darbo and Mönch's fixed point theorems). Finally we give an illustrative example in the last section. We initiate the study of fractional q-difference inclusions on infinite dimensional Banach spaces. [ABSTRACT FROM AUTHOR]

Kannan maps have inspired a branch of metric fixed point theory devoted to the extension of the classical Banach contraction principle. The study of these maps in modular vector spaces was attempted timidly and was not successful. In this work, we look at this problem in the variable exponent sequence spaces ℓ p (·) . We prove the modular version of most of the known facts about these maps in metric and Banach spaces. In particular, our results for Kannan nonexpansive maps in the modular sense were never attempted before. [ABSTRACT FROM AUTHOR]