Schauder fixed point theorem in spaces with global nonpositive curvature.
Second-order differential inclusions with Lipschitz right-hand sides.
Semicompatibility and fixed point theorems in an unbounded -metric space.
Sequence of iterates of generalized contractions
Sets in the ranges of nonlinear accretive operators in Banach spaces
Let X be a real Banach space and G ⊂ X open and bounded. Assume that one of the following conditions is satisfied: (i) X* is uniformly convex and T:Ḡ→ X is demicontinuous and accretive; (ii) T:Ḡ→ X is continuous and accretive; (iii) T:X ⊃ D(T)→ X is m-accretive and Ḡ ⊂ D(T). Assume, further, that M ⊂ X is pathwise connected and such that M ∩ TG ≠ ∅ and . Then . If, moreover, Case (i) or (ii) holds and T is of type , or Case (iii) holds and T is of type , then M ⊂ TG. Various results of Morales,...
Set-valued maps with fixed and coincidence points.
Singular nonlinear elliptic equations in .
Singular -Laplacian third-order BVPs with derivative dependance
This work is devoted to the existence of solutions for a class of singular third-order boundary value problem associated with a -Laplacian operator and posed on the positive half-line; the nonlinearity also depends on the first derivative. The upper and lower solution method combined with the fixed point theory guarantee the existence of positive solutions when the nonlinearity is monotonic with respect to its arguments and may have a space singularity; however no Nagumo type condition is assumed....
Sizes of sets and some fixed point theorems
Small functions and iterative methods
Iterative methods based on small functions are used both to show local surjectivity of certain operators and a fixed point property of mappings on scales of complete metric spaces.
Solution du problème de point fixe de Schauder
We give an affirmative answer to Schauder's fixed point question.
Solution of nonlinear integral equations via fixed point of generalized contractive condition
Solution to Fredholm integral inclusions via ( F, δ b )-contractions
We present sufficient conditions for the existence of solutions of Fredholm integral inclusion equations using new sort of contractions, named as multivalued almost F -contractions and multivalued almost F -contraction pairs under ı-distance, defined in b-metric spaces. We give its relevance to fixed point results in orbitally complete b-metric spaces. To rationalize the notions and outcome, we illustrate the appropriate examples.
Solvability of an Infinite System of Singular Integral Equations
2000 Mathematics Subject Classification: 45G15, 26A33, 32A55, 46E15.Schauder's fixed point theorem is used to establish an existence result for an infinite system of singular integral equations in the form: (1) xi(t) = ai(t)+ ∫t0 (t − s)− α (s, x1(s), x2(s), …) ds, where i = 1,2,…, α ∈ (0,1) and t ∈ I = [0,T]. The result obtained is applied to show the solvability of an infinite system of differential equation of fractional orders.
Solving some nonlinear equations by successive approximations.
Some algebraic fixed point theorems for multi-valued mappings with applications
In this paper, some algebraic fixed point theorems for multi-valued discontinuous operators on ordered spaces are proved. These theorems improve the earlier fixed point theorems of Dhage (1988, 1991) Dhage and Regan (2002) and Heikkilä and Hu (1993) under weaker conditions. The main fixed point theorems are applied to the first order discontinuous differential inclusions for proving the existence of the solutions under certain monotonicity condition of multi-functions.
Some applications of the coincidence degree for set-contractions to functional differential equations of neutral type
Some approximate fixed point theorems without continuity of the operator using auxiliary functions
We introduce partial generalized convex contractions of order and rank using some auxiliary functions. We present some results on approximate fixed points and fixed points for such class of mappings having no continuity condition in -complete metric spaces and -complete metric spaces. Also, as an application, some fixed point results in a metric space endowed with a binary relation and some approximate fixed point results in a metric space endowed with a graph have been obtained. Some examples...
Some common fixed point results for rational type contraction mappings in partially ordered metric spaces
The purpose of this paper is to establish some common fixed point results for -nondecreasing mappings which satisfy some nonlinear contractions of rational type in the framework of metric spaces endowed with a partial order. Also, as a consequence, a result of integral type for such class of mappings is obtained. The proved results generalize and extend some of the results of J. Harjani, B. Lopez, K. Sadarangani (2010) and D. S. Jaggi (1977).
Some common fixed point theorems for biased mappings
Some common fixed point theorems in normed spaces are proved using the concept of biased mappings- a generalization of compatible mappings.