Fixed Point Theorems for Multivalued Mappings Involving -Function

We obtain some fixed point theorems with error estimates for multivalued mappings satisfying a new --contractive type condition. Our theorems generalize many existing fixed point theorems, including some fixed point theorems proved for --contractive type conditions

Generalized Twisted (α, β)-ψ-Contractive Mappings of Integral Type on Spaces with Two Metrics

Abstract In this paper, we extend and generalize the notion of twisted (α, β)-ψ-contractive maps on spaces with two metrics. Our results provide a compact form for both type of results related to twisted (α, β)-ψ-contractive mappings and generalized contractions on spaces with two metrics. We establish new fixed point theorems which generalize the Banach contraction principle and so many other results in the literature. An example is constructed to support our results

Fixed Point Theorems for Multivalued Mappings Involving α

We obtain some fixed point theorems with error estimates for multivalued mappings satisfying a new α-ψ-contractive type condition. Our theorems generalize many existing fixed point theorems, including some fixed point theorems proved for α-ψ-contractive type conditions

A Mizoguchi–Takahashi Type Fixed Point Theorem in Complete Extended <i>b</i>-Metric Spaces

In this paper, we prove a new fixed point theorem for a multi-valued mapping from a complete extended b-metric space U into the non empty closed and bounded subsets of U, which generalizes Nadler&#8217;s fixed point theorem. We also establish some fixed point results, which generalize our first result. Furthermore, we establish Mizoguchi&#8722;Takahashi&#8217;s type fixed point theorem for a multi-valued mapping from a complete extended b-metric space U into the non empty closed and bounded subsets of U that improves many existing results in the literature

On Some New Fixed Point Results in Complete Extended <i>b</i>-Metric Spaces

In this paper, we specified a method that generalizes a number of fixed point results for single and multi-valued mappings in the structure of extended b-metric spaces. Our results extend several existing ones including the results of Aleksic et al. for single-valued mappings and the results of Nadler and Miculescu et al. for multi-valued mappings. Moreover, an example is given at the end to show the superiority of our results

On Multivalued Fuzzy Contractions in Extended b-Metric Spaces

In this paper, we establish a Hausdorff metric over the family of nonempty closed subsets of an extended b-metric space. Thereafter, we introduce the concept of multivalued fuzzy contraction mappings and prove related α-fuzzy fixed point theorems in the context of extended b-metric spaces that generalize Nadler’s fixed point theorem as well as many preexisting results in the literature. Further, we establish α-fuzzy fixed point theorems for Ćirić type fuzzy contraction mappings as a generalization of previous results. Moreover, we give some examples to support the obtained results

On Controlled Rectangular Metric Spaces and an Application

In this paper, we introduce the notion of controlled rectangular metric spaces as a generalization of rectangular metric spaces and rectangular b-metric spaces. Further, we establish some related fixed point results. Our main results extend many existing ones in the literature. The obtained results are also illustrated with the help of an example. In the last section, we apply our results to a common real-life problem in a general form by getting a solution for the Fredholm integral equation in the setting of controlled rectangular metric spaces