Search

Abstract In this article, we introduce the structure of a new extended cone b-metric-like space over a Banach algebra. In this generalized space, we define the notion of generalized Reich-type mappings and prove a fixed point result. We also prove a fixed point result using α ∗ − ψ $\alpha^{\ast}-\psi$ multivalued contraction and provide some of its consequences. Finally, we furnish with applications to establish the validity of our results.

Abstract The survey of the available literature shows that a lot of important invariant point problems of Banach and Heilpern types have been examined in both metric and quasimetric spaces. However, a handful of the existing results employed the recent approaches of interpolative contractions. Therefore, based on the new idea of interpolation techniques in fixed point theory, this article studies new notions of L-fuzzy contractions and investigates conditions for the existence of L-fuzzy fixed points for such mappings. On the fact that fixed points of point-to-point mappings satisfying interpolative-type contraction are not always unique, whence making the concepts more fitted for invariant point results of crisp set-valued maps, new multi-valued analogues of the key findings put forward in this work are derived. Comparative illustrations, which indicate the preeminence of the results presented herein, are constructed. From application viewpoint, one of the theorems so obtained is employed to introduce new solvability conditions of Fredholm-type integral inclusions.

Abstract The purpose of this study is to establish fixed-point results for new interpolative contraction mappings in the setting of Busemann space involving a convex hull. To illustrate our findings, we also offer helpful and compelling examples. Finally, the theoretical results are applied to study the existence of solutions to fractional Navier–Stokes and fractional-functional differential equations as applications.

Abstract In this article, we obtain some fixed-point results involving α-admissibility for multivalued F-contractions in the framework of partial b $\mathfrak{b}$ -metric spaces. Appropriate illustrations are provided to support the main results. Finally, an application is developed by demonstrating the existence of a solution to an integral equation.

Abstract The logical progression from the constant order differential equations is the field of variable-order differential equations. Such equations can frequently give a more succinct description of problems in the real world. In light of this, we therefore take into account a class of coupled boundary value problems under variable-order differentiation. By utilizing the fixed-point techniques of Banach and Schauder, we investigate the existence and uniqueness of solutions to the proposed problem. Also, sufficient results are documented for the necessary needs. Furthermore, some stability results based on the ideas of Ulam, Hyers, and Rassias are elaborated upon. Ultimately, appropriate examples and in-depth analysis are presented to support our results.

Abstract In this manuscript, a novel general class of contractions, called Jaggi–Suzuki-type hybrid (G-α-ϕ)-contraction, is introduced and some fixed point theorems that cannot be deduced from their akin in metric spaces are proved. The dominance of this family of contractions is that its contractive inequality can be specialized in various manners, depending on multiple parameters. Nontrivial comparative examples are constructed to validate the assumptions of our obtained theorems. Consequently, a number of corollaries that reduce our result to some prominent results in the literature are highlighted and analyzed. Additionally, we examine Ulam-type stability and well-posedness for the new contraction proposed herein. Finally, one of our obtained corollaries is applied to set up unprecedented existence conditions for solution to a class of integral equations. For future aspects of our results, an open problem is noted concerning the discretized population balance model, whose solution may be analyzed using the techniques established herein.

Abstract The objective of this article is to incorporate the concept of the Ostrowski inequality with the Atangana–Baleanu fractional integral operator. A novel integral identity for twice-differentiable functions is established after a rigorous investigation of several basic definitions and existing ideas related to inequalities and fractional calculus. Following that, numerous Ostrowski-type inequalities are provided based on this identity, which uses Mittag–Leffler as its kernel structure. Some specific applications, such as q-digamma functions and modified Bessel functions, are also investigated. Choosing s = 1 $s=1$ , we also analyze new results for convex functions as special cases. Our findings corroborate some well-documented inequalities.

Abstract The objective of the present research is to establish and prove some new common fuzzy fixed-point theorems for fuzzy set-valued mappings involving Θ-contractions in a complete metric space. For this purpose, a novel integral-type contraction condition is applied to obtain these results. In this way, several useful and classical results have been generalized. Moreover, a concrete example is created to furnish our results. An application to stochastic Volterra integral equations has been given to enhance the validity of our results.

Abstract The purpose of this paper is to consider some F-contraction mappings in a dualistic partial metric space and to provide sufficient related conditions for the existence of a fixed point. The obtained results are extensions of several ones existing in the literature. Moreover, we present examples and an application to support our results.

Abstract The interaction among phytoplankton and zooplankton is one of the most important processes in ecology. Discrete-time mathematical models are commonly used for describing the dynamical properties of phytoplankton and zooplankton interaction with nonoverlapping generations. In such type of generations a new age group swaps the older group after regular intervals of time. Keeping in observation the dynamical reliability for continuous-time mathematical models, we convert a continuous-time phytoplankton–zooplankton model into its discrete-time counterpart by applying a dynamically consistent nonstandard difference scheme. Moreover, we discuss boundedness conditions for every solution and prove the existence of a unique positive equilibrium point. We discuss the local stability of obtained system about all its equilibrium points and show the existence of Neimark–Sacker bifurcation about unique positive equilibrium under some mathematical conditions. To control the Neimark–Sacker bifurcation, we apply a generalized hybrid control technique. For explanation of our theoretical results and to compare the dynamics of obtained discrete-time model with its continuous counterpart, we provide some motivating numerical examples. Moreover, from numerical study we can see that the obtained system and its continuous-time counterpart are stable for the same values of parameters, and they are unstable for the same parametric values. Hence the dynamical consistency of our obtained system can be seen from numerical study. Finally, we compare the modified hybrid method with old hybrid method at the end of the paper.

Abstract In this paper, we derive some common α-fuzzy fixed point results for fuzzy mappings under generalized almost F $\mathcal{\mathbf{F}}$ -contractions in the context of a controlled metric space, which generalize many preexisting results in the literature. As an application, we establish some multivalued fixed point results. For justification of our results, we provide a nontrivial example.

Abstract A remarkably large number of hypergeometric (and generalized) functions and a variety of their extensions have been presented and investigated in the literature by many authors. In this paper, we introduce five new hypergeometric functions in four variables and then establish several recursion formulas for these new functions. Some interesting particular cases and consequences of the main results are also considered.

Abstract The main purpose of this paper is to present some fixed-point results for a pair of fuzzy dominated mappings which are generalized V-contractions in modular-like metric spaces. Some theorems using a partial order are discussed and also some useful results to graphic contractions for fuzzy-graph dominated mappings are developed. To explain the validity of our results, 2D and 3D graphs have been constructed. Also, applications are provided to show the novelty of our obtained results and their usage in engineering and computer science.

Abstract In this paper, we study the behavior of L ( ω , C ) $L_{ ( \omega,C ) }$ -contraction mappings and establish some results on common fixed circles and discs. We explain the significance of our main theorems through examples and applications.

Abstract We introduce double and triple F-expanding mappings. We prove related fixed point theorems. Based on our obtained results, we also prove the existence of a solution for fractional type differential equations by using a weaker condition than the sufficient small Lipschitz constant studied by Mehmood and Ahmad (AIMS Math. 5:385–398, 2019) and Hanadi et al. (Mathematics 8:1168, 2020). As applications, we ensure the existence of a unique solution of a boundary value problem for a second-order differential equation.

Abstract This paper aims to present the concept of multi-valued mappings in fuzzy cone metric spaces and prove some basic lemmas, a Hausdorff metric, and fixed point results for set-valued fuzzy cone-contraction and for multi-valued fuzzy cone-contraction mappings. We prove a fixed point theorem for multi-valued rational type fuzzy cone-contractions in fuzzy cone metric spaces. Our results extend and improve some results given in the literature.

Abstract The aim of this work is to establish results in fixed point theory for a pair of fuzzy dominated mappings which forms a rational fuzzy dominated V-contraction in modular-like metric spaces. Some results via a partial order and using the graph concept are also developed. We apply our results to ensure the existence of a solution of nonlinear Volterra-type integral equations.

Abstract This paper provides two wide classes of contractions, which are obtained by using notions of α s p $\alpha _{s^{p}} $ -admissibility and the rich set of C-class functions in the setting of a complete b-metric-like space under more general contractive conditions. An application is provided and many known results in the literature can be derived.

Abstract In this manuscript, some fixed point results for generalized contractive type mappings under mild conditions in the setting of double controlled metric spaces (in short, η ℷ ν $\eta _{\gimel }^{\nu }$ -metric spaces) are obtained. Moreover, some related consequences dealing with a common fixed point concept and nontrivial examples to support our results are presented. Ultimately, we use the theoretical results to discuss the existence and uniqueness of solutions of 2D Volterra integral equations, Riemann–Liouville integrals and Atangana–Baleanu integral operators are given.

Abstract In this paper, we initiate a new extension of b-metric spaces, called controlled metric-like spaces, by changing the condition [ ℘ ( s , r ) = 0 ⇔ s = r ] by [ ℘ ( s , r ) = 0 ⇒ s = r ] $$ \bigl[\wp (s,r)=0 \Leftrightarrow s=r\bigr]\quad \text{by } \bigl[\wp (s,r)=0 \Rightarrow s=r\bigr] $$ and that means basically we may have a non-zero self-distance. We prove some fixed point theorems which generalize many results in the literature. Also, we present an interesting application to illustrate our results by considering controlled metric-like spaces endowed with a graph.

Abstract In this paper, we introduce the notion of an α–ζ̃– –Pata contraction that combines well-known concepts, such as the Pata contraction, the E-contraction and the simulation function. Existence and uniqueness of a fixed point of such mappings are investigated in the setting of a complete metric space. An example is stated to indicate the validity of the observed result. At the end, we give an application on the solution of nonlinear fractional differential equations.

Abstract The aim of this paper is to present several fixed-point results for L-contractive multivalued mappings involving θ-functions in the class of metric spaces. We also give some examples in support of the related concepts and presented results. A homotopy result is also provided.

Abstract In this paper, we establish that every controlled metric space (X,dα) $(X, d_{\alpha })$ induces a Hausdorff controlled metric (Hα,CLD(X)) $(\textit{H}_{\alpha }, \textit{CLD}(X))$ on the class of closed subsets of X which is also complete if (X,dα) $(X, d_{\alpha })$ is complete. Furthermore, we define multivalued almost F-contractions on Hausdorff controlled metric spaces and prove some fixed point results.

Abstract The notion of nonlinear (Fs,L) $(\mathcal{F}_{s}, \mathcal{L})$-contractive multivalued operators is initiated and some related fixed point results are considered. We also give an example to show the validity of obtained theoretical results. Our results generalize many existing ones in the literature.

Abstract The goal of this work is to introduce an extended interpolative Ćirić–Reich–Rus type contraction by the approach of Wardowski. We establish some related fixed point results (for single and multivalued-mappings). Some examples are presented to illustrate the main result. Moreover, we give an application to integral equations.

Abstract In this paper, we obtain sufficient conditions for the nonexistence of global solutions for some classes of q-difference inequalities. Our approach is based on the weak formulation of the problem, a particular choice of the test function, and some q-integral inequalities.

Abstract A Lyapunov-type inequality is established for the anti-periodic fractional boundary value problem (CDaα,ψu)(x)+f(x,u(x))=0,a0 $\psi'(x)>0$, x∈[a,b] $x\in[a,b]$, Daα,ψC ${}^{C}D_{a}^{\alpha,\psi}$ is the ψ-Caputo fractional derivative of order α, and f:[a,b]×R→R $f: [a,b]\times\mathbb{R}\to\mathbb{R}$ is a given function. Next, we give an application of the obtained inequality to the corresponding eigenvalue problem.

Abstract Based on a recent paper of Beg and Pathak (Vietnam J. Math. 46(3):693–706, 2018), we introduce the concept of Hq+ $\mathcal{H}_{q}^{+}$-type Suzuki multivalued contraction mappings. We establish a fixed point theorem for this type of mappings in the setting of complete weak partial metric spaces. We also present an illustrated example. Moreover, we provide applications to a homotopy result and to an integral inclusion of Fredholm type. Finally, we suggest open problems for the class of 0-complete weak partial metric spaces, which is more general than complete weak partial metric spaces.

Abstract The aim of this work is to establish a new fixed point theorem for generalized contraction mappings with respect to w-distances in complete metric spaces. An illustrative example is provided to advocate the usability of our results. Also, we give a numerical experiment for approximating a fixed point in these examples. As an application, the received results are used to summarize the existence and uniqueness of the solution for nonlinear integral equations and nonlinear fractional differential equations of Caputo type.