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In this paper, we introduce the novel concept of generalized distance denoted as J θ and call it an extended b-generalized pseudo-distance. With the help of this generalized distance, we define a generalized point to set distance J θ (u , H ★) , a generalized Hausdorff type distance and a P J θ -property of a pair (H ★ , K ★) of nonempty subsets of extended b-metric space (U ★ , ρ θ). Additionally, we establish several best proximity point theorems for multi-valued contraction mappings of Nadler type defined on b-metric spaces and extended b-metric spaces. Our findings generalize numerous existing results found in the literature. To substantiate the introduced notion and validate our main results, we provide some concrete examples. [ABSTRACT FROM AUTHOR]

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 a novel form of interpolative convex contraction and develop some new theorems by utilizing the progressive method of interpolative convex contractions. We also obtain some fixed point results for a Suzuki convex contraction in orbitally S-complete F-metric spaces. The second purpose of this research is to evaluate the effectiveness of the fixed point approach in solving fractional differential equations with boundary conditions. [ABSTRACT FROM AUTHOR]

The target of this manuscript is to introduce new symmetric fractional α-β-η-Y-contractions and prove some new fixed point results for such contractions in the setting of Mb-metric space. Moreover, we derive some results for said contractions on closed ball of mentioned space. The existence of the solution to a fractional-order differential equation with one boundary stipulation will be discussed. [ABSTRACT FROM AUTHOR]

In this research, we establish some new fixed-point results for a symmetric coupled dominated fuzzy mapping satisfying a new advanced contraction on a closed ball in the setting of complete fuzzy metric spaces. In addition, the new notion of hybrid fuzzy-graph-dominated mappings introduced in fuzzy metric spaces achieves some new advanced fuzzy fixed-point problems. Some new definitions and illustrative examples are given to validate our new findings. Lastly, to demonstrate the originality of our new results, we present an application to the Fredholm-type integral equation. [ABSTRACT FROM AUTHOR]

The objective of this paper is to introduce a new motif of α ∗ -ψ-Λ-contraction multivalued mappings, some novel fixed-point and coincidence-point results for this contraction will be investigated in the scope of F-metric spaces, and some examples are given to illustrate our main results and we derive the existence and uniqueness of a solution of a functional equation to support our main result. [ABSTRACT FROM AUTHOR]

The purpose of this article is to introduce an ordered implicit relation that can be used for the existence of fixed points of new contractions defined in cone A-metric spaces. We investigate a fixed-point method for proving the existence of Urysohn integral equation solutions. We prove an homotopy result by the application of obtained fixed-point theorem. The hypothesis is demonstrated with examples. [ABSTRACT FROM AUTHOR]

The manuscript is an extension of the investigations concerning θ-contractions which have been newly proposed in (Jleli and Samet in J. Inequal. Appl. 2014:38, 2014). The authors generalize the notion of θ-contractions to the case of nonlinear θ b -contraction mappings and prove multi-valued fixed point theorems based on the b-Bianchini–Grandolfi gauge function in b-metric spaces. The manuscript consists of a tangible example which displays the motivation for such investigations. The work is compiled by the application of the proposed nonlinear θ b -contractions to Liouville–Caputo fractional differential equations. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the conditions for the existence of the common fixed points of generalized contractions in the partial b -metric spaces endowed with an arbitrary binary relation. We establish some unique common fixed-point theorems. The obtained results may generalize and improve earlier fixed-point results. We provide examples to illustrate our findings. As an application, we discuss the common solution to the system of boundary value problems. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new idea of best proximity point of F-contraction on a closed ball and obtain new theorems in a complete metric space. That is why this outcome becomes useful for contraction of a mapping on a closed ball instead of the whole space. At the same time, some comparative examples are constructed which establish the superiority of our results. Our results that have come into being give a proof of 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]

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]