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We define a notion of degree for a class of perturbations of nonlinear Fredholm maps of index zero between infinite-dimensional real Banach spaces. Our notion extends the degree introduced by Nussbaum for loca...
In reply to a problem of Jean Leray (application of the Nielsen theory to differential equations), two main approaches are presented. The first is via Poincaré's translation operator, while the second one is b...
The iterative schemes with some control conditions for a family of finite nonexpansive mappings are established in a Banach space. The main theorem improves results of Jung and Kim (also Bauschke). Our results...
We prove strong convergence theorems of Mann's type and Halpern's type for resolvents of accretive operators with compact domains and apply these results to find fixed points of nonexpansive mappings in Banach...
-contractions, and
-subweakly commuting maps
We present common fixed point theory for generalized contractive
-subweakly commuting maps and obtain some results on invariant approximation.
A new applicable Leray-Schauder alternative is presented for weakly-strongly sequentially continuous maps. This result is then used to establish a general existence principle for operator equations.
In 1979, Ishikawa proved a strong convergence theorem for finite families of nonexpansive mappings in general Banach spaces. Motivated by Ishikawa's result, we prove strong convergence theorems for infinite fa...
We prove that each analytic self-map of the open unit disk which interpolates between certain
-tuples must have a fixed point.
Let
be an open subset of a real uniformly smooth Banach space
. Suppose
We study the regularization methods for solving equations with arbitrary accretive operators. We establish the strong convergence of these methods and their stability with respect to perturbations of operators...
Much has been written about systems in which each constant is a solution and each solution approaches a constant. It is a small step to conjecture that functions promoting such behavior constitute harmless per...
Suppose
,
are manifolds,
...
We present existence results for general variational inequalities without monotonicity or coercivity assumptions. It relies on a Leray-Schauder degree approach and provides additional information about the loc...
spaces and
-trees
We show that if
is a bounded open set in a complete
space
As is well known, in any infinite-dimensional Banach space one may find fixed point free self-maps of the unit ball, retractions of the unit ball onto its boundary, contractions of the unit sphere, and nonzero...
Assume that
is a proper map of a connected
-manifold
It is well known that some of the properties enjoyed by the fixed point index can be chosen as axioms, the choice depending on the class of maps and spaces considered. In the context of finite-dimensional real...
Using continuous selections, we establish some existence results about the zeros of weakly continuous operators from a paracompact topological space into the dual of a reflexive real Banach space.
We prove a fixed-point-like theorem for multivalued mappings defined on the finite Cartesian product of Grassmannian manifolds and convex sets. Our result generalizes two different kinds of theorems: the fixed...
The solvability of nonlinear equations has awakened great interest among mathematicians for a number of centuries, perhaps as early as the Babylonian culture (3000-300 B.C.E.). However, we intend to bring to o...
Let
be a nonempty, bounded, closed, and convex subset of a Banach space. We show that the iterates of a typical element (in the sense o...
-distance
Using the notion of
-distance, we prove several fixed point theorems, which are generalizations of fixed point theorems by Kannan, Meir-...
A continuation principle of Leray-Schauder type is presented for contractions with respect to a gauge structure depending on the homotopy parameter. The result involves the most general notion of a contractive...
In metric spaces, single-valued self-maps and multimaps with closed images are considered and fixed point and coincidence point theorems for such maps have been obtained without using the (extended) Hausdorff ...
Let
be a finite connected complex and
a fibration over a c...
We introduce a generalized form of the Fan-Browder fixed point theorem and apply to game-theoretic and economic equilibrium existence problem under the more generous restrictions. Consequently, we state some o...
In the class of quasi-contractive operators satisfying Zamfirescu's conditions, the most used fixed point iterative methods, that is, the Picard, Mann, and Ishikawa iterations, are all known to be convergent t...
-Lienard systems
We examine
-Lienard systems driven by the vector
-Laplacian ...
With the aid of the simplicial approximation property, we show that every admissible multivalued map from a compact convex subset of a complete metric linear space into itself has a fixed point. From this fact...
Given a finite family of nonexpansive self-mappings of a Hilbert space, a particular quadratic functional, and a strongly positive selfadjoint bounded linear operator, Yamada et al. defined an iteration scheme...
Convergence theorems for approximation of common fixed points of a finite family of asymptotically pseudocontractive mappings are proved in Banach spaces using an averaging implicit iteration process.
We propose, in the general setting of topological spaces, a definition of two-dimensional oriented cell and consider maps which possess a property of stretching along the paths with respect to oriented cells. ...
We present several new fixed point results for admissible self-maps in extension-type spaces. We also discuss a continuation-type theorem for maps between topological spaces.
We first introduce an iterative sequence for finding fixed points of relatively nonexpansive mappings in Banach spaces, and then prove weak and strong convergence theorems by using the notion of generalized pr...
We obtain sufficient conditions for the existence of an equilibrium pair for a particular constrained generalized game as an application of a best proximity pair theorem.
We show that a discrete fixed point theorem of Eilenberg is equivalent to the restriction of the contraction principle to the class of non-Archimedean bounded metric spaces. We also give a simple extension of ...
The Nielsen number is a homotopic invariant and a lower bound for the number of coincidences of a pair of continuous functions. We give two homotopic (topological) definitions of this number in general situati...
The reduced Lefschetz number, that is,
where
denotes the L...
2022 Citation Impact
0.970 - SNIP (Source Normalized Impact per Paper)
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