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In this article, fixed point results for self-mappings in the setting of two metrics satisfying FF-lipschitzian conditions of rational-type are proved, where FF is considered as a semi-Wardowski function with constant τ∈R\tau \in {\mathbb{R}} instead of τ>0\tau \gt 0. Two metrics have been considered, one as an incomplete while the other is orbitally complete. The mapping is taken to be orbitally continuous from one metric to another. Some examples are provided to validate our results. For applications, we present existence results for the solutions of a new type of ABC-fractional boundary value problem.

This paper presents the following AB-Caputo fractional boundary value problem 0 ABC D α u (ς) = (ς , u (ς)) , ς ∈ [ 0 , 1 ] with integral-type boundary conditions u (0) = 0 = u ″ (0) , γ u (1) = λ ∫ 0 1 g 1 (ϰ) u (ϰ) d ϰ , of order 2 < α ≤ 3. Schauder and Krasnoselskii's fixed point theorems are used to find existence results. Uniqueness is obtained via the Banach contraction principle. To investigate the stability of a given problem, Hyers–Ulam stability is discussed. An example is provided to validate our results. [ABSTRACT FROM AUTHOR]

The pursuit of understanding fixed points and their applications has been significantly enhanced through the exploration of multi-valued mappings. This article introduces the concept of multi-valued mappings within C*-algebra-valued metric spaces. By utilizing the lower bound property, this study extends the Banach, Kannan, and Chatterjea theorems for multi-valued mappings in such spaces (for example see [14]). Moreover, the application aspect is enriched through the provision of an existence result for AB-Caputo partial hyperbolic type fractional differential inclusions. This result enhances the applicability of such inclusions, bridging the gap between theory and application. The paper concludes by offering few open problems that set the stage for future researchers in this field. The results presented here not only generalize numerous findings in the existing literature but also offer new insights into this area of research. [ABSTRACT FROM AUTHOR]

In this article a novel concept of C*-algebra-valued measure of non-compactness is defined. Using this concept, the well known fixed point theorems of Darbo, Sadovskii and Krasnoslskii are generalized. We present non-trivial examples and applications to validate the real utilization of our results. [ABSTRACT FROM AUTHOR]

In this article some new fixed point and hybrid coincidence point theorems for multivalued mappings satisfying generalized contractive conditions have been proved in generalized metric spaces. Some nontrivial examples are given to support our main theorems. As application, a differential inclusion problem for heat conduction in metals has been given, using our main result, we prove the existence of solutions to the given differential inclusion problem. [ABSTRACT FROM AUTHOR]