we first obtain some properties of a fundamentally nonexpansive self-mapping on a nonempty subset of a banach space and next show that if the banach space is having the opial condition, then the fixed points set of such a mapping with the convex range is nonempty. in particular, we establish that if the banach space is uniformly convex, and the range of such a mapping is bounded, closed and con...

We characterize the holomorphic mappings f between complex Banach spaces that may be written in the form f = T ◦ g, where g is another holomorphic mapping and T belongs to a closed surjective operator ideal.

Characterization of the mapping properties such as boundedness, compactness, measure of non-compactness and estimates of the approximation numbers of Hardy-type integral operators in Banach function spaces are given.

In this paper, we introduce and study a system of mixed variational-like inclusions and a system of proximal operator equations in Banach spaces which contains variational inequalities, variational inclusions, resolvent equations, system of variational inequalities and system of variational inclusions in the literature as special cases. It is established that the system of mixed variational-lik...

Let C be a compact convex subset of a Hausdorff topological vector space (E , τ) and σ another Hausdorff vector topology in E . We establish an approximate fixed point result for sequentially continuous maps f : (C , σ) → (C , τ). As application, we obtain the weakapproximate fixed point property for demicontinuous self-mapping weakly compact convex sets in general Banach spaces and use this to...

We construct global-in-time solutions for semilinear parabolic rough partial differential equations. work on a scale of Banach spaces tailored to the controlled path approach and derive suitable priori estimates solution which do not contain quadratic terms.

In this paper, we present a new iterative scheme for finding a common element of the solution set F of the split feasibility problem and the fixed point set F(T) of a right Bregman strongly quasi-nonexpansive mapping T in p-uniformly convex Banach spaces which are also uniformly smooth. We prove strong convergence theorem of the sequences generated by our scheme under some appropriate condition...

In this article, we introduce iterative methods (implicit and explicit) for finding a common fixed point set of a countable family of strict pseudo-contractions, which is a unique solution of some variational inequality. Furthermore, we prove the strong convergence theorems of such iterative scheme in a q-uniformly smooth Banach space which admits a weakly sequentially continuous generalized du...

Let A + B be the pointwise (Minkowski) sum of two convex subsets A and B of a Banach space. Is it true that every continuous mapping h : X → A + B splits into a sum h = f + g of continuous mappings f : X → A and g : X → B? We study this question within a wider framework of splitting techniques of continuous selections. Existence of splittings is guaranteed by hereditary invertibility of linear ...