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We introduce a C' iric' type contraction principle in a vector-valued b-metric space that generalizes Perov's contraction principle. We investigate the possible conditions on the mappings W, E: G → G (G is a non-empty set), for which these mappings admit a unique common fixed point in G subject to a nonlinear operator F: Pm → Rm. We illustrate the hypothesis of our findings with examples. We consider an infectious disease model represented by the system of delay integrodifferential equations and apply the obtained fixed point theorem to show the existence of a solution to this model. [ABSTRACT FROM AUTHOR]

The focus of this paper is to conduct a comprehensive analysis of the advancements made in the understanding of Interpolative contraction, building upon the ideas initially introduced by Karapinar in 2018. In this paper, we develop the notion of Interpolative contraction mappings to the case of non-linear Kannan Interpolative, Riech Rus Ćirić interpolative and Hardy–Roger Interpolative contraction mappings based on controlled function, and prove some fixed point results in the context of controlled metric space, thereby enhancing the current understanding of this particular analysis. Furthermore, we provide a concrete example that illustrates the underlying drive for the investigations presented in this context. An application of the proposed non-linear Interpolative-contractions to the Liouville–Caputo fractional derivatives and fractional differential equations is provided in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we introduce orthogonal multivalued contractions, which are based on the recently introduced notion of orthogonality in the metric spaces. We construct numerous fixed point theorems for these contractions. We show how these fixed point theorems aid in the generalization of a number of recently published findings. Additionally, we offer a theorem that establishes the existence of a fractional differential equation's solution. [ABSTRACT FROM AUTHOR]

The idea of best proximity points of the fuzzy mappings in fuzzy metric space was intorduced by Vetro and Salimi. We introduce a new type of proximal contractive condition that ensures the existence of best proximity points of fuzzy mappings in the fuzzy complete metric spaces. We establish certain best proximity point theorems for such proximal contractions. We improve and generalize the fuzzy proximal contractions by introducing Ψ , Φ -fuzzy proximal contractions and Ψ , Φ -fuzzy proximal interpolative contractions. The obtained results improve and generalize many best proximity point theorems published earlier. Moreover, we provide many nontrivial examples to validate our best proximity point theorem. [ABSTRACT FROM AUTHOR]

This paper presents a systematic investigation of an extension of the developments concerning the q-contractions, which were proposed in 2014 by Jleli and Samet. This paper generalizes the notion of the q-contractions to the case of non-linear qL-contraction mappings, and prove multi-valued fixed point results in b-metric-like spaces. The paper also includes a tangible example, which displays the motivation for such investigations as those presented here. This paper is completed by giving an application of the proposed non-linear qL-contractions to the Liouville-Caputo fractional derivatives and fractional differential equations. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the new idea of α-C-class function and establish new fixed point results in a complete metric space. It can be stated that the results that have come into being give substantial generalizations and improvements of several well known results in the existing comparable literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the new idea of α-C-class function and establish new fixed point results in a complete metric space. It can be stated that the results that have come into being give substantial generalizations and improvements of several well known results in the existing comparable literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a notion of hybrid pair (f; T), which is α*-admissible with respect to η for generalized multivalued Geraghty F-contraction mappings and obtain coincidence and common fixed point results for such mappings. We provide some examples to support our results and give applications to dynamic programming and integral equations. Our results provide extension as well as substantial generalizations and improvements of several well known results in the existing comparable literature. [ABSTRACT FROM AUTHOR]

This paper is a continuation of the investigations of F-contractions. The aim of this article is to extend the concept of Ciric type F-contraction on a closed ball. We presented the notion of F-contraction on a closed ball and introduced a new approach of fixed point theorems for Fcontraction on a closed ball in a complete metric space. Our results are very useful for the contraction of the mapping only on closed ball instead of the whole space. Some comparative examples are constructed which illustrate the superiority of our results. Our results provide extension as well as substantial generalizations and improvements of several well-known results in the existing comparable literature. [ABSTRACT FROM AUTHOR]

The aim of this paper is to establish Ćirić type fixed point results for multi-valued mappings satisfying generalized α-ψ-contractive conditions on closed ball in complete metric space. As an application, we derive some new fixed point theorems for Ćirić type ψ-graphic contractions and rational - graphic contractions defined on metric space endowed with a graph as well as ordered metric space. Examples has been constructed to demonstrate the novelty of our results. Our results unify, extend and generalize several comparable results in the existing literature. [ABSTRACT FROM AUTHOR]

The purpose of the present paper is to continue the study of fixed point theory in complete metric spaces. Wardowski [Fixed Point Theory Appl. 2012: 94] introduced a new type of contraction called F-contraction and proved a fixed point result in complete metric spaces, which in turn generalize the Banach contraction principle. The aim of this paper is to extend the concept of F-contraction into generalized F-contraction. An example and application are given to illustrate the usability of the main result. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of dualistic contraction of rational type. We prove some fixed point theorems for ordered mappings satisfying above mentioned contraction. We give examples to illustrate the importance of these results. We present an application of our fixed point result to show the existence of solution of integral equations. [ABSTRACT FROM AUTHOR]

The aim of this paper is to establish fixed point results for semi fixed α*-admissible multivalued mappings satisfying generalized locally α*-ψ-contractive conditions in complete dislocated metric space. As an application, we derive some new fixed point theorems for preordered metric space and metric space endowed with a graph. Example has been constructed to demonstrate the novelty of our results. Our results unify, extend and generalize several comparable results in the existing literature. [ABSTRACT FROM AUTHOR]

Recently Abbas [M. Abbas, Fixed Point Theory, 13 (2012), 3-10] introduced the concept of f-almost contraction which in turn extended the class of multivalued almost contraction mapping and obtained coincidence point results for this new class of mappings. The aim of this paper is to introduce the notion of dynamic process for generalized (f, L)--almost F--contraction mappings and to obtain coincidence and common fixed point results for such process. It is worth mentioning that our results do not rely on the commonly used range inclusion condition. We provide some examples to support our results. As an application of our results, we obtain the existence and uniqueness of solutions of dynamic programming and integral equations. Our results provide extension as well as substantial generalizations and improvements of several well known results in the existing comparable literature. [ABSTRACT FROM AUTHOR]

In this paper, we present new fixed point theorems for Kannan type Fp-contraction and Kannan type (α η;GFp)-contraction on a closed ball contained in a complete partial metric space. Some comparative examples are constructed to illustrate the significance of these results. Our results provide substantial generalizations and improvements of several well known results existing in the comparable literature. [ABSTRACT FROM AUTHOR]

The aim of this paper is to establish some new fixed point results for Ćirić type α-η-GF-contraction in a complete metric space. We extend the concept of F-contraction and introduce the notion Ćirić type α-η-GF-contraction. An example is given to demonstrate the novelty of our work. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce some new fixed point results of Hardy-Rogers-type for α-η-GF-contraction in a complete metric space. We extend the concept of F-contraction into an α-η-GF-contraction of Hardy-Rogers-type. An example has been constructed to demonstrate the novelty of our results. [ABSTRACT FROM AUTHOR]

In this article, following the approach of F-contractions, we establish a common fixed point theorem for a pair of self-mappings satisfying F-contraction of rational type in complete metric spaces. An example is constructed to illustrate this result. An application to system of integral equations is presented. [ABSTRACT FROM AUTHOR]