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In this paper, we propose a modified general inertial Mann algorithm and prove that it generates a sequence which converges weakly to a fixed point of a nonexpansive mapping in Hilbert spaces. Moreover, by using the viscosity method, we introduce a general inertial viscosity algorithm and prove that it generates a sequence which converges strongly to a common fixed point of a countable family of nonexpansive operators. We also derive schemes for solving constrained convex optimization, monotone inclusion, and nonsmooth convex optimization problems. Finally, we apply one of our proposed algorithms to solve image restoration problem. [ABSTRACT FROM AUTHOR]

In this work, we analyse the class of strictly pseudocontractive mappings in general metric spaces by providing a comprehensive and appropriate definition of a strictly pseudocontractive mapping, which serves as a natural extension of the existing notion. Moreover, we establish its various characterizations and explore several significant properties of these mappings in relation to fixed point theory in CAT(0) spaces. Specifically, we establish that these mappings are Lipschitz continuous, satisfying the demiclosedness-type property, and possessing a closed convex fixed point set. Furthermore, we show that the fixed points of the mappings can be effectively approximated using an iterative scheme for fixed points of nonexpansive mappings. The results in this work contribute to a deeper understanding of strictly pseudocontractive mappings and their applicability in the context of fixed point theory in metric spaces. [ABSTRACT FROM AUTHOR]

An inertial Mann algorithm will be presented in this article with the purpose of approximating a fixed point of a nonexpansive mapping on a Hadamard manifold. Any sequence that is generated by using the proposed approach, under suitable assumptions, converges to fixed points of nonexpansive mappings. The proposed method is also dedicated to solving inclusion and equilibrium problems. Lastly, we give a number of computational experiments that show how well the inertial Mann algorithm works and how it compares to other methods. [ABSTRACT FROM AUTHOR]

In this manuscript, we investigate a nonlinear SIQR pandemic model to study the behavior of covid-19 infectious diseases. The susceptible, infected, quarantine and recovered classes with fractal fractional Atangana-Baleanu-Caputo (ABC) derivative is studied. The non-integer order ℘ and fractal dimension q in the proposed system lie between 0 and 1. The existence and uniqueness of the solution for the considered model are studied using fixed point theory, while Ulam-Hyers stability is applied to study the stability analysis of the proposed model. Further, the Adams-Bashforth numerical technique is applied to calculate an approximate solution of the model. It is observed that the analytical and numerical calculations for different fractional-order and fractal dimensions confirm better converging effects of the dynamics as compared to an integer order. [ABSTRACT FROM AUTHOR]

This paper provides iterative solutions, via some variants of the extragradient approximants, associated with the pseudomonotone equilibrium problem (EP) and the fixed point problem (FPP) for a finite family of η-demimetric operators in Hilbert spaces. The classical extragradient algorithm is embedded with the inertial extrapolation technique, the parallel hybrid projection technique and the Halpern iterative methods for the variants. The analysis of the approximants is performed under suitable set of constraints and supported with an appropriate numerical experiment for the viability of the approximants. [ABSTRACT FROM AUTHOR]

In this paper, we incorporate proximal point algorithm with some convex combination techniques to approximate a minimizer and a common fixed point of a family of multi-valued mappings in Hadamard spaces. We prove -convergence and strong convergence theorems for a convex lower semi-continuous function and multi-valued quasi-nonexpansive mappings. Furthermore, we apply our results to find mean, median and solve equilibrium problems in Hadamard spaces. Finally, we give two numerical examples, one in a non-Hilbert space with a non-convex functional and the other in a Hilbert space, to demonstrate the convergence of the proposed method. [ABSTRACT FROM AUTHOR]

Fractional calculus has been very popular due to the application in real world problems. This paper aimed to investigate the existence, uniqueness and Ulam stability for nonlinear fractional pantograph differential equations with generalized nonlocal boundary conditions involving Hilfer fractional derivative. The analysis were done through Banach and Kranoselskii's fixed point theorems. Finally, example are given to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

We present a new approach for finding a minimal value of an arbitrary function assuming only its continuity. The process avoids verifying Lagrange- or KKTconditions. The method enables us to obtain a Brouwer fixed point (of a continuous function mapping from a cube into itself). [ABSTRACT FROM AUTHOR]

Recently, researchers are showing more interest on both modular vector spaces and modular function spaces. Looking at the number of results it is pertinent to say that, exploration in this direction especially in the area of fixed point theory and applications is still ongoing, many good results can still be unveiled. As a contribution from our part, we study some fixed point results in modular vector spaces associated with order relation. As an application, we were able to study the existence of fixed point(s) of both depolarizing quantum operation and Markov operators through modular functions/modular spaces. The awareness on the importance of quantum theory and Economics globally were the sole motivations of the application choices in our work. Our work complement the existing results. In fact, it adds to the number of application areas that modular vector/function spaces covered. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new discontinuous operator and investigate the existence and uniqueness of fixed points for the operators in complete metric spaces. We also provide rate of convergence and data dependency of S-iterative scheme for a fixed point of the discontinuous operators in Banach spaces. Moreover, we prove the estimation Collage theorems and compare error estimate between data dependency and Collage theorems. Numerical examples are provided to support our results. [ABSTRACT FROM AUTHOR]

The aim of this manuscript is to improve certain results established in a recent paper of Imdad et al on the existence of a common fixed point for contractive mappings in fuzzy metric spaces. Further, we generalize and extend some common fixed point theorems due to Ali and Imdad and some fixed point theorems due to Mihet to the case of fuzzy metric‐like spaces. We also furnish an illustrative example to demonstrate the validity of the hypotheses and degree of generality of our main result. [ABSTRACT FROM AUTHOR]

In this paper, we modify the proximal point algorithm for finding common fixed points in CAT(0) spaces for nonlinear multivalued mappings and a minimizer of a convex function and prove Δ‐convergence of the proposed algorithm. A numerical example is presented to illustrate the convergence result. Our results improve and extend the corresponding results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce graphic contraction mappings in b-metric spaces and establish some fixed point theorems in the aforesaid space. Appropriate graphs are presented to visualize related definitions and concepts. On the other hand, some examples are presented to verify the authenticity and effectiveness of the established results. Our results generalize and extend some pioneer results existing in the literature. Moreover, applications to existence of solution for ordinary differential equations and for integral equations are also established to show the adequacy of our results. [ABSTRACT FROM AUTHOR]

In this paper, we proved some existence theorems of fixed points for monotone nonspreading mappings T in a Banach space E with the partial order ·. In order to finding a fixed point of such a mapping T, moreover we proved the convergence theorem of Mann iterative schemes under the condition 1P nÆ1 n(1¡n) Æ1, which contain n Æ 1 nÅ1 as a special case. [ABSTRACT FROM AUTHOR]

In this paper, we first prove a result that gives a sufficient condition for the convergence of the sequences in the b2-metric space. Next, we give some fixed point theorems in the b2-metric space. Some of our results are the corresponding generalizations of the known results in the b2-metric space, which is confirmed by some examples. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and prove fixed point results for some classes of ℑ‐contraction mappings on Pompeiu‐Hausdorff functionals in dislocated b‐metric spaces. We illustrate an example and graph to support our main results. We present the generalized Ulam‐Hyers stability of fixed point inclusion. Finally, we have applied our results to find a solution of Fredholm‐type integral inclusion in dislocated b‐metric spaces. Our results generalize some recent results and extend several theorems in the literature. [ABSTRACT FROM AUTHOR]

The main purpose of this study is to establish some coincidence and common fixed point theorems for 2 self‐mappings via the condition of implicit function on metric spaces provided with arbitrary binary relation. In our results, the main theorems are the generalized version of the literatures, and we also give some examples to guarantee our main results. Moreover, we show that the result to guarantee a coincidence point which are more useful than the previous results of Banach's contraction which cannot be applied. Furthermore, we include some consequences for proving the corollary, which satisfied several well‐known contractions that are obtained from the main results. [ABSTRACT FROM AUTHOR]

Inspired by the work of Dakjum et al. [Eshi, D., Das, P. K. and Debnath, P., Coupled coincidence and coupled common fixed point theorems on a metric space with a graph, Fixed Point Theory Appl., 37 (2016), 1-14], we introduce a new class of G-f-contraction mappings in complete fuzzy metric spaces endowed with a directed graph and prove some existence results for coupled coincidence and coupled common fixed point theorems of this type of contraction mappings in complete fuzzy metric spaces endowed with a directed graph. [ABSTRACT FROM AUTHOR]

The purpose of this article is to investigate a projection algorithm for solving a fixed point problem of a closed multi-valued Bregman quasi-strict pseudocontraction and an equilibrium problem of a bifunction. Strong convergence of the projection algorithm is obtained without any compact assumption in a reflexive Banach space. As applications, monotone variational inequality problems are considered. Finally, a numerical simulation example is presented for demonstrating the feasibility and convergence of the algorithm proposed in main result. [ABSTRACT FROM AUTHOR]

In this paper, we will present some fixed point results for two classes of generalized contractions of Boyd-Wong type in partial b-metric spaces. More precisely, the structure of the paper is the following. In section one, we present some useful notions and results. The aim of section two is to introduce the concepts of Boyd-Wong F-contractions of type A and of type B and establish some new common fixed point results in partial b-metric spaces. We show the validity and superiority of our main results by suitable examples which are visualized by corresponding surfaces and related graphs. In section three, we correct some slip-ups in some recent papers. Finally, in section four, two applications to integral equation and periodic boundary value problem are included which make effective the new concepts and results. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new modified proximal point algorithm involving fixed point iteration for nonexpansive mappings in CAT(1) spaces. Under some mild conditions, we prove that the sequence generated by our iterative algorithm Δ-converges to a common solution between certain convex optimization and fixed point problems. [ABSTRACT FROM AUTHOR]

In this paper, we establish some fixed point results for fuzzy mappings in a complete dislocated b-metric space. Our results generalize and extend the results of Joseph et al. (SpringerPlus 5:Article ID 217, 2016). We also give examples to support our results, and applications relating the results to a fixed point for multivalued mappings and fuzzy mappings are studied. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of cone b-metric spaces over Banach algebras and present some quadruple random coincidence points and quadruple random common fixed point theorems for nonlinear operators in such spaces. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and prove some classes of fuzzy contractive mappings with altering distance function via α and βκ-admissible mappings in the fuzzy metric spaces. We also give some example and graph which demonstrate the validity of the hypotheses of our main results. Our results improve and extend several previously known fixed point theorems of the existing literature. As an application to our main result a fixed point for contraction mappings of integral type in fuzzy metric spaces are presented. [ABSTRACT FROM AUTHOR]

In this paper, we consider a common solution of three problems in Hilbert spaces including the split generalized equilibrium problem, the variational inequality problem and fixed point problem. For finding the solution, we present a new iterative method and prove the strongly convergence theorem under mild conditions. Moreover, some numerical examples are given in the last section. [ABSTRACT FROM PUBLISHER]

In this paper, we obtain the best proximity point theorem for α-proximal contraction of the first and second kinds in Banach spaces by using fixed point theorems. Also, we mention an example for justification of our results. [ABSTRACT FROM AUTHOR]

In this article, we introduce a new concept of contraction called F-Khan-contractions and prove a fixed point theorem concerning this contraction which generalizes the results announced by Khan [M. S. Khan, Rend. Inst. Math. Univ. Trieste., 8 (1976), 69-72], Fisher [B. Fisher, Riv. Math. Univ. Parma., 4 (1978), 135-137], and Piri et al. [H. Piri, S. Rahrovi, P. Kumam, J. Math. Computer Sci., 17 (2017), 76-83]. An example and application for the solution of certain integral equations are given to illustrate the usability of the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce notions of (α, θ)-generalized rational contraction conditions and investigate the existence of the fixed point of such mappings on complete metric spaces. To illustrate our result we also construct an example. [ABSTRACT FROM AUTHOR]

In this paper, by using the concept of the a-Garaghty contraction, we introduce the new notion of the a-Q-Garaghty type contraction and prove some fixed point results for this contraction in partial metric spaces. Also, we give some examples and applications to illustrate the main results. [ABSTRACT FROM AUTHOR]

In paper, we prove some common fixed point theorems for the pair of self-mappings with the g-quasi-condition in modular metric spaces. Also, we modify and prove some common fixed point theorems by using the (CLRg)-property along with the weakly compatible mapping. Finally, we give some applications on integral equations to illustrate our main results. [ABSTRACT FROM AUTHOR]

In this paper, we prove the generalized UHR stability of a quartic functional equations f(2x + y) + f(2x - y) = 4f(x + y) + 4f(x - y) + 24f(x) - 6f(y) via the extensive studies of fixed point theory. Our results are obtained in the framework of modular spaces by the modular which is l.s.c. and convex. [ABSTRACT FROM AUTHOR]

In this paper, we prove some strong and Δ-convergence theorems of the modified S-iteration for (α, β)-generalized hybrid mappings in CAT(0) spaces. Our results improve and extend the corresponding recent results announced in [1] and some papers. [ABSTRACT FROM AUTHOR]

We present some existence and convergence results for monotone α-nonexpansive mappings in partially ordered hyperbolic metric spaces. A recent result of Bin Dehaish and Khamsi [Browder and Göhde fixed point theorem for monotone nonexpansive mappings, Fixed Point Theory Appl. 2016, 2016:20] is complemented. [ABSTRACT FROM AUTHOR]

In this paper, we present some results on the existence of coincidence and periodic point of F-contractive mappings in the framework of modular metric spaces endowed with a graph. We also present an application to partial differential equations in order to support the theoretical results. [ABSTRACT FROM AUTHOR]

The notion of a modular metric on an arbitrary set and the corresponding modular spaces, generalizing classical modulars over linear spaces like Orlicz spaces, were recently introduced. In this paper we investigate some fixed-point theorems in modular metric spaces. [ABSTRACT FROM AUTHOR]

The aim of this work is to establish some new fixed point theorems for generalized F-Suzuki-contraction mappings in complete b-metric spaces. [ABSTRACT FROM AUTHOR]

In this paper, we prove some existence theorems of fixed points of a monotone nonexpansive mapping T in a Banach space E with the partial order '≤', where a such mapping may be discontinuous. In particular, in finite dimensional spaces, such a mapping T has a fixed point in E if and only if the sequence $\{T^{n}0\}$ is bounded in E. In order to find a fixed point of such a mapping T, we prove the weak convergence of the Mann iteration scheme under the condition $\sum_{n=1}^{\infty}\beta_{n}(1-\beta_{n})=\infty$, which entails $\beta _{n}=\frac{1}{n+1}$ as a special case. [ABSTRACT FROM AUTHOR]

In this manuscript, common fixed point results for self-mappings satisfying generalized weak integral type contraction in the setting of G-metric space are established. Using the derived results, some applications to the systems of non-linear integral and fractional differential equations are also discussed. [ABSTRACT FROM AUTHOR]

In this article, recognizing the innovative concept of complex valued fuzzy set due to Ramot et al. [1], we introduce the notion of complex valued fuzzy metric spaces. Several allied topological aspects for complex valued fuzzy metric spaces are also defined which fortify the concept. Moreover the complex valued fuzzy version of some celebrated and essential results from metric spaces including Banach contraction principle and the main theorem of Jungck [2] are established. Additionally some fixed point theorems satisfying certain rational expressions are proved. [ABSTRACT FROM AUTHOR]

Recently, Kumam, et al. in [P. Kumam, J. Martinez-Moreno, A. Roldán, C. Roldán, J. Inequal. Appl., 2014 (2014), 7 pages] proved some tripled fixed point theorems in fuzzy normed spaces. In this paper, we give a new version of the result of Kumam, et al. by removing some restrictions. In our result, the t-norms are not required to be the minimum ones. [ABSTRACT FROM AUTHOR]

In this paper, we state and prove Wardowski type fixed point theorems in metric space by using a modified generalized F-contraction maps. These theorems extend other well-known fundamental metrical fixed point theorems in the literature (Dung and Hang in Vietnam J. Math. 43:743-753, and Piri and Kumam in Fixed Point Theory Appl. 2014:210, , etc.). Examples are provided to support the usability of our results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce iterative algorithms for finding a zero of set-valued accretive operators by the viscosity approximation method based on Meir-Keeler-type contractions in a reflexive Banach space which admits a weakly continuous duality mapping. We obtain some strong convergence theorems under suitable conditions. As applications, we apply our results for finding common fixed point of nonexpansive semigroups and for solving equilibrium problem, optimization problem, and variational inequalities. [ABSTRACT FROM AUTHOR]

In this paper, we present an iterative scheme for Bregman strongly nonexpansive mappings in the framework of Banach spaces. Furthermore, we prove the strong convergence theorem for finding common fixed points with the set of solutions of an equilibrium problem. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the two new concepts of an α-type almost- F-contraction and an α-type F Suzuki contraction and prove some fixed point theorems for such mappings in a complete metric space. Some examples and an application to a nonlinear fractional differential equation are given to illustrate the usability of the new theory. [ABSTRACT FROM AUTHOR]

We introduce a new hybrid projection method in mathematical programming for finding a common element of the set of common fixed points of a countable family of relatively quasi-nonexpansive mappings, the set of the variational inequality for an-inverse-strongly monotone operator, the set of solutions of the mixed equilibrium problem and a zero of a maximal monotone operator in the framework of a real Banach space. We obtain a strong convergence theorem for the sequences generated by this process in a 2-uniformly convex and uniformly smooth Banach space. Furthermore, we give some numerical examples which support our main theorem in the last part. [ABSTRACT FROM AUTHOR]

In this paper, we prove common coupled fixed point theorems under a Geraghty-type condition using monotone instead of the often used mixed monotone property. Also we give some sufficient conditions for the uniqueness of a common coupled fixed point. An example illustrating our results is provided. [ABSTRACT FROM AUTHOR]

The object of this paper is to extend the concept of β-admissible for multivalued mappings due to Mohammadi et al. [B. Mohammadi, S. Rezapour and N. Shahzad, Some results on fixed points of α-ψ-Ciric generalized multifunctions, Fixed Point Theory and Applications 2013 (2013), 24] to fuzzy mappings and utilize this concept to prove a common α-fuzzy fixed point theorem for a pair of fuzzy mappings. We also give illustrative example which demonstrate the validity of the hypotheses of our results. Some related results to common fixed point for multivalued mappings are also derived from the main result. [ABSTRACT FROM AUTHOR]

In this paper, we introduce new implicit and explicit iterative methods for finding a common fixed point set of an infinite family of strict pseudo-contractions by the sunny nonexpansive retractions in a real q-uniformly and uniformly convex Banach space which admits a weakly sequentially continuous generalized duality mapping. Then we prove the strong convergence under mild conditions of the purposed iterative scheme to a common fixed point of an infinite family of strict pseudo-contractions which is a solution of some variational inequalities. Furthermore, we apply our results to study some strong convergence theorems in Lp and ℓp spaces with 1 < p <∞. Our results mainly improve and extend the results announced by Ceng et al. (Comput. Math. Appl. 61:2447-2455, 2011) and many authors from Hilbert spaces to Banach spaces. Finally, we give some numerical examples for support our main theorem in the end of the paper. [ABSTRACT FROM AUTHOR]