From metric spaces to partial metric spaces

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Some new fixed point results in non-Archimedean fuzzy metric spaces

In this paper, we introduce the notions of fuzzy (α,β,ϕ)-contractive mapping, fuzzy α-φ-ψ-contractive mapping and fuzzy α-β-contractive mapping and establish some results of fixed point for this class of mappings in the setting of non-Archimedean fuzzy metric spaces. The results presented in this paper generalize and extend some recent results in fuzzy metric spaces. Also, some examples are given to support the usability of our results

Common fixed points of generalized Mizoguchi-Takahashi type contractions in partial metric spaces

We give some common fixed point results for multivalued mappings in the setting of complete partial metric spaces. Our theorems extend and complement analogous results in the existing literature on metric and partial metric spaces. Finally, we provide an example to illustrate the new theory

Multi-valued F-contractions and the solution of certain functional and integral equations

Wardowski [Fixed Point Theory Appl., 2012:94] introduced a new concept of contraction and proved a fixed point theorem which generalizes Banach contraction principle. Following this direction of research, we will present some fixed point results for closed multi-valued F-contractions or multi-valued mappings which satisfy an F-contractive condition of Hardy-Rogers-type, in the setting of complete metric spaces or complete ordered metric spaces. An example and two applications, for the solution of certain functional and integral equations, are given to illustrate the usability of the obtained results

A note on some fundamental results in complete gauge spaces and application

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Some notes on a second-order random boundary value problem

We consider a two-point boundary value problem of second-order random differential equation. Using a variant of the α-ψ-contractive type mapping theorem in metric spaces, we show the existence of at least one solution

From Caristi's Theorem to Ekeland's Variational Principle in -Complete Metric-Like Spaces

We discuss the extension of some fundamental results in nonlinear analysis to the setting of0σ-complete metric-like spaces. Then, we show that these extensions can be obtained via the corresponding results in standard metric spaces

common fixed point theorems for weakly compatible maps satisfying a general contractive condition

We introduce a new generalized contractive condition for four mappings in the framework of metric space. We give some common fixed point results for these mappings and we deduce a fixed point result for weakly compatible mappings satisfying a contractive condition of integral type

Fixed point and homotopy results for mixed multi-valued mappings in 0-complete partial metric spaces

We give sufficient conditions for the existence of common fixed points for a pair of mixed multi-valued mappings in the setting of 0-complete partial metric spaces. An example is given to demonstrate the usefulness of our results over the existing results in metric spaces. Finally, we prove a homotopy theorem via fixed point results

A remark on differentiable functions with partial derivatives in Lp

We consider a definition of p, δ-variation for real functions of several variables which gives information on the differentiability almost everywhere and the absolute integrability of its partial derivatives on a measurable set. This definition of p, δ-variation extends the definition of n-variation of Malý and the definition of p-variation of Bongiorno. We conclude with a result of change of variables based on coarea formula