Existence of Fixed Points in Fuzzy Strong b-Metric Spaces

In the present research, modern fuzzy technique is used to generalize some conventional and latest results. The objective of this paper is to construct and prove some fixed-point results in complete fuzzy strong b-metric space. Fuzzy strong b-metric (sb-metric) spaces have very useful properties such as openness of open balls whereas it is not held in general for b-metric and fuzzy b-metric spaces. Due to its properties, we have worked in these spaces. In this way, we have generalized some well-known fixed-point theorems in fuzzy version. In addition, some interesting examples are constructed to illustrate our results.

COMMON FIXED POINT THEOREM FOR TWO MAPPINGS IN bi-b-METRIC SPACE

In this paper we have used the concept of bi-metric space and intoduced the concept of bi-b-metric space. our objective is to obtain the common fixed point theorems for two mappings on two different b-metric spaces induced on same set X. In this paper we prove that on the set X two b-metrics are defined to form two different b-metric spaces and the two mappings defined on X have unique common fixed point.

Common Fixed Point Theorems for Weakly Contractions in Rectangular b -Metric Spaces with Supportive Applications

In this manuscript, two new classes of generalized weakly contractions are introduced and common fixed point results concerning the new contractions are proved in the context of rectangular b -metric spaces. Also, some examples are included to present the validity of our theorems. As an application, we provide the existence and uniqueness of solution of an integral equation.

Solutions and stability for p-Laplacian differential problems with mixed type fractional derivatives

In this note, the main emphasis is to study two kinds of high-order fractional p-Laplacian differential equations with mixed derivatives, which include Caputo type and Riemann–Liouville type fractional derivative. Based on fixed point theorems on the cone, the existence-uniqueness of positive solutions for equations and two iterative schemes to uniformly approximate the unique solutions are discussed theoretically. What’s more, the sufficient conditions for stability of the equations are given. Some exact examples are further provided to verify the analytical results at the end of the article.

Some periodic and fixed point theorems on quasi-b-gauge spaces

The notions of a quasi-b-gauge space $(U,\textsl{Q}_{s ; \Omega })$ ( U , Q s ; Ω ) and a left (right) $\mathcal{J}_{s ; \Omega }$ J s ; Ω -family of generalized quasi-pseudo-b-distances generated by $(U,\textsl{Q}_{s ; \Omega })$ ( U , Q s ; Ω ) are introduced. Moreover, by using this left (right) $\mathcal{J}_{s ; \Omega }$ J s ; Ω -family, we define the left (right) $\mathcal{J}_{s ; \Omega }$ J s ; Ω -sequential completeness, and we initiate the Nadler type contractions for set-valued mappings $T:U\rightarrow Cl^{\mathcal{J}_{s ; \Omega }}(U)$ T : U → C l J s ; Ω ( U ) and the Banach type contractions for single-valued mappings $T: U \rightarrow U$ T : U → U , which are not necessarily continuous. Furthermore, we develop novel periodic and fixed point results for these mappings in the new setting, which generalize and improve the existing fixed point results in the literature. Examples validating our obtained results are also given.

An Approach of Integral Equations in Complex-Valued b -Metric Space Using Commuting Self-Maps

This paper is aimed at establishing some unique common fixed point theorems in complex-valued b -metric space under the rational type contraction conditions for three self-mappings in which the one self-map is continuous. A continuous self-map is commutable with the other two self-mappings. Our results are verified by some suitable examples. Ultimately, our results have been utilized to prove the existing solution to the two Urysohn integral type equations. This application illustrates how complex-valued b -metric space can be used in other types of integral operators.

Multivalued and random version of Perov fixed point theorem in generalized gauge spaces

In this paper, we present some random fixed point theorems in complete gauge spaces. We establish then a multivalued version of a Perov–Gheorghiu’s fixed point theorem in generalized gauge spaces. Finally, some examples are given to illustrate the results.