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The main aim of this paper is to obtain some new common fixed point theorems for Geraghty's type contraction mappings using the monotone property with two metrics and to give some examples to illustrate the main results. Further, by using our main results, we prove some results about multidimensional common fixed points. Our results generalize and extend some recent results given by Kadelburg et al. (Fixed Point Theory Appl. 2015:27, 2015) and Choudhurya and Kundu (J. Nonlinear Sci. Appl. 5:259-270, 2012). [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of generalized cyclic contraction pairs in b-metric spaces and establish some fixed point theorems for such pairs. Also, we give some examples to illustrate the main results which properly generalizes some results given by some authors in literature. Further, by using the main results, we prove some common fixed point results for generalized contraction pairs in partially ordered b-metric spaces. Our results generalize and improve the result of Shatanawi and Postolache (Fixed Point Theory Appl. 2013:60, 2013) and several well-known results given by some authors in metric and b-metric spaces. [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]

We prove a fixed point result in orbitally $$0$$ -complete partial metric spaces, using a variant of almost contractive condition that involves a rational expression. Also, a common fixed point result in $$0$$ -complete partial metric spaces is obtained. Several consequences are deduced and examples are presented, showing that the given result can be used for proving the existence of (common) fixed points when some known results fail. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of $(\alpha,\theta,k)$-contraction multi-valued mappings and establish some fixed point results for such mappings by using some control functions due to Jleli et al. (J. Inequal. Appl. 2014:439, 2014) in metric spaces and furnish some interesting examples to illustrate our main results. Also, we give some fixed point results in metric spaces endowed with a graph. Our results generalize and extend recent results given by some authors. [ABSTRACT FROM AUTHOR]

In this paper, we prove some fixed point theorems for weakly compatible mappings in fuzzy metric spaces employing common limit range property with implicit relations. We also furnish some illustrative examples to support our main results. As an application to our main result, we derive a fixed point theorem for four finite families of self-mappings which can be utilized to derive common fixed point theorems involving any finite number of mappings. Our results improve and extend a host of previously known results including the ones contained in the paper of Gopal et al. (2011). [ABSTRACT FROM AUTHOR]

We study Ulam-Hyers stability and the well-posedness of the fixed point problem for new type of generalized contraction mapping, so called α-λ-contraction mapping. The results in this paper generalize and unify several results in the literature such as the Banach contraction principle. [ABSTRACT FROM AUTHOR]

We extend the notion of generalized weakly contraction mappings due to Choudhury et al. (2011) to generalized α-β-weakly contraction mappings. We show with examples that our new class of mappings is a real generalization of several known classes of mappings. We also establish fixed point results for such mappings in metric spaces. Applying our new results, we obtain fixed point results on ordinary metric spaces, metric spaces endowed with an arbitrary binary relation, and metric spaces endowed with graph. [ABSTRACT FROM AUTHOR]

We study the generalizedUlam-Hyers stability, the well-posedness, and the limit shadowing of the fixed point problem for new type of generalized contraction mapping, the so-called α-β-contraction mapping. Our results in this paper are generalized and unify several results in the literature as the result of Geraghty (1973) and the Banach contraction principle. [ABSTRACT FROM AUTHOR]

The aim of this paper is to obtain some new integral type fixed point theorems for nonself weakly compatible mappings in symmetric spaces satisfying generalized (ψ, φ)-contractive conditions employing the common limit range property We furnish some interesting examples which support our main theorems. Our results generalize and extend some recent results contained in Imdad et al. (2013) to symmetric spaces. Consequently, a host of metrical common fixed theorems are generalized and improved. In the process, we also derive a fixed point theorem for four finite families of mappings which can be utilized to derive common fixed point theorems involving any number of finite mappings. [ABSTRACT FROM AUTHOR]

We introduce the class of mixed equilibriumproblemswith theweakly relaxed α-monotone bi-function in Banach spaces.Using the KKM technique, we obtain the existence of solutions for mixed equilibrium problem with weakly relaxed α-monotone bi-function in Banach spaces.The results presented in this paper extend and improve the corresponding results in the existing literature. [ABSTRACT FROM AUTHOR]

We introduce two new concepts of weakly relaxed η-α monotone mappings and weakly relaxed η-α semimonotone mappings. Using the KKM technique, the existence of solutions for variational-like problems with weakly relaxed η-α monotone mapping in reflexive Banach spaces is established. Also, we obtain the existence of solution for variational-like problems with weakly relaxed η-α semimonotone mappings in arbitrary Banach spaces by using the Kakutani-Fan-Glicksberg fixed-point theorem. [ABSTRACT FROM AUTHOR]

We introduce the concept of the generalized wα-contraction mappings and establish the existence of fixed point theorem for such mappings by using the properties of w-distance and α-admissible mappings. We also apply our result to coincidence point and common fixed point theorems in metric spaces. Further, the fixed point theorems endowed with an arbitrary binary relation are also derived from our results. Our results generalize the result of Kutbi, 2013, and several results in the literature. [ABSTRACT FROM AUTHOR]

The objective of this paper is to emphasize the role of "common limit range property" to ascertain the existence of common fixed point in fuzzy metric spaces. Some illustrative examples are furnished which demonstrate the validity of the hypotheses and degree of utility of our results. We derive a fixed point theorem for four finite families of self-mappings which can be utilized to derive common fixed point theorems involving any finite number of mappings. As an application to ourmain result, we prove an integraltype fixed point theorem in fuzzy metric space. Our results improve and extend a host of previously known results including the ones contained in Imdad et al. (2012). [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of fuzzy (F, φ,β-ψ)-contractive mappings in fuzzy metric spaces and utilize the same to prove some existence and uniqueness fuzzy φ-fixed point results in both M-complete and G-complete fuzzy metric spaces. The obtained results extend, generalize and improve some relevant results of the existing literature. An illustrative example is utilized to demonstrate the usefulness and effectiveness of our results. [ABSTRACT FROM AUTHOR]

We extend the recent results of the coupled fixed point theorems of Cho et al. (2012) by weakening the concept of the mixed monotone property. We also give some examples of a nonlinear contraction mapping, which is not applied to the existence of the coupled fixed point by the results of Cho et al. but can be applied to our results. The main results extend and unify the results of Cho et al. and many results of the coupled fixed point theorems. [ABSTRACT FROM AUTHOR]

This article is written due to a small gap in our published paper. In this erratum, we point out and fix the problem to set our existed results at the best of their perfection. [ABSTRACT FROM AUTHOR]

In this work, we improve the concept of the Banach contractive condition in the setting of D -generalized metric spaces and obtain φ -fixed point results in such spaces. Our φ -fixed point results improve and extend some recently obtained results in several abstract metric spaces. Moreover, some example and numerical results are also presented. [ABSTRACT FROM AUTHOR]

In this work, we present the viscosity method for the implicit double midpoint rule for finding the fixed points of nonexpansive mappings in real Hilbert spaces. The strong convergence theorem of this method is proved under some specific assumption imposed on the control parameters. Also, we present some numerical results which are presented to illustrate the proposed method and convergence results. Moreover, we provide the applications to the variational inequality problems, constrained convex minimization problems, nonlinear evolution equations, and Fredholm integral equations. [ABSTRACT FROM AUTHOR]

The choice behavior model is the model which describes the spiritual process of thinking which is concerned with the process of judging the merits of the numerous options and making the decision to determine one of them for action. The aim of this paper is to analyze the one specific type of choice behavior model for the learning process of the paradise fish. The existence and uniqueness results of the solution of the proposed choice behavior model are investigated via the fixed point tool. [ABSTRACT FROM AUTHOR]

The purpose of this work is to establish new fixed point theorems for generalized contraction mappings with respect to w-distances in complete metric spaces by using the concept of a weak altering distance function. Two illustrative examples are provided to advocate the usability of our results. Also, we present 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 Fredholm integral equations. [ABSTRACT FROM AUTHOR]

In this work, we introduce the notion of a Z R -contraction mapping, where R is an binary relation on its domain, which improves upon the idea of Khojasteh et al. (Filomat 29:1189–1194, 2015). We establish some fixed point results for Z R -contraction mappings in complete metric spaces endowed with a transitive relation and also give two illustrative examples. Moreover, we show that N-th order fixed point theorems are derived from our main results. As an application, we apply our main result to study a class of nonlinear matrix equation. Finally, as numerical experiments, we approximate the definite solution of a nonlinear matrix equation using MATLAB. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Abstract The main aim of this work is to unify different classes of fuzzy contractive mappings by introducing a new class of fuzzy contractive mappings called fuzzy Z -contractive mappings. For this new class of mappings, suitable conditions are framed to ensure the existence of fixed point in M -complete fuzzy metric spaces (in the sense of George and Veeramani). A comprehensive set of examples are presented to support the claim. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to study the Boyd-Wong type fixed point result in the F-metric context and apply it to obtain some existence and uniqueness criteria of solution(s) to a second order initial value problem and a Caputo fractional differential equation. We substantiate our obtained result by finding a suitable non-trivial example. [ABSTRACT FROM AUTHOR]

Abstract: We prove some coincidence and common fixed point theorems for two hybrid pairs of mappings in Menger spaces satisfying a strict contractive condition. An illustrative example is given to support the genuineness of our extension besides deriving some related results. Then, we establish the corresponding common fixed point theorems in metric spaces. Finally, we utilize our main result to obtain the existence of a common solution for a system of Volterra type integral equations. [Copyright &y& Elsevier]

A theory of chemical graphs is a part of mathematical chemistry concerned with the effects of connectedness in chemical graphs. Several researchers have studied the solutions of fractional differential equations using the concept of star graphs. They employed star graphs because their technique requires a central node with links to adjacent vertices but no edges between nodes. The purpose of this paper is to extend the method's range by introducing the concept of an octane graph, which is an essential organic compound having the formula C8H18. In this manner, we analyze a graph with vertices annotated by 0 or 1, which is influenced by the structure of the chemical substance octane, and formulate a fractional boundary value problem on each of the graph's edges. We use the Schaefer and Krasnoselskii fixed point theorems to investigate the existence of solutions to the presented boundary value problems in the framework of the Caputo fractional derivative. Finally, two examples are provided to highlight the importance of our results in this area of study., Competing Interests: The authors have declared that no competing interests exist.

This paper aims to suggest a time-fractional S P E P I P A I P S P H P R P model of the COVID-19 pandemic disease in the sense of the Atangana-Baleanu-Caputo operator. The proposed model consists of six compartments: susceptible, exposed, infected (asymptomatic and symptomatic), hospitalized and recovered population. We prove the existence and uniqueness of solutions to the proposed model via fixed point theory. Furthermore, a stability analysis in the context of Ulam-Hyers and the generalized Ulam-Hyers criterion is also discussed. For the approximate solution of the suggested model, we use a well-known and efficient numerical technique, namely the Toufik-Atangana numerical scheme, which validates the importance of arbitrary order derivative ϑ and our obtained theoretical results. Finally, a concise analysis of the simulation is proposed to explain the spread of the infection in society., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© 2022 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.)

We study the generalized Ulam-Hyers stability, the well-posedness, and the limit shadowing of the fixed point problem for new type of generalized contraction mapping, the so-called α-β-contraction mapping. Our results in this paper are generalized and unify several results in the literature as the result of Geraghty (1973) and the Banach contraction principle.

We extend the notion of generalized weakly contraction mappings due to Choudhury et al. (2011) to generalized α-β-weakly contraction mappings. We show with examples that our new class of mappings is a real generalization of several known classes of mappings. We also establish fixed point results for such mappings in metric spaces. Applying our new results, we obtain fixed point results on ordinary metric spaces, metric spaces endowed with an arbitrary binary relation, and metric spaces endowed with graph.