In this paper we prove strong convergence theorems for approximating the fixed point of Lipschitzian semigroup and infinite family of nonexpansive mappings with respect to finite family of sequence {μi,n} ∞ i=1,n=1 of left strong regular invariant means and Meir-Keeler type contraction in uniformly convex and smooth Banach spaces. Our result extend and improve many recent results.

Necessary and sufficient conditions are obtained for the Lipschitzian stability of local solutions to finite-dimensional parameterized optimization problems in a very general setting. Properties of prox-regularity of the essential objective function and positive definiteness of its coderivative Hessian are the key to these results. A previous characterization of tilt stability comes out as a sp...

The theory of differential inclusions provides certain sufficient conditons for the uniqueness of Filippov solutions such as one-sided Lipschitzian property or maximal monotone condition. When applied to piecewise affine dynamical systems, these conditions impose rather strong conditions. In this paper, we provide less restrictive conditions for uniqueness of Filippov solutions for the bimodal ...

In this paper, we study a coupled fully hybrid system of (k,Φ)–Hilfer fractional differential equations equipped with non-symmetric (k,Φ)–Riemann-Liouville (RL) integral conditions. To prove the existence and uniqueness results, use Krasnoselskii Perov fixed-point theorems Lipschitzian matrix in context generalized Banach space (GBS). Moreover, Ulam–Hyers (UH) stability solutions is discussed b...

Given a bounded domain Ω ⊂ R, we prove that if f : R → R is a C function whose gradient is Lipschitzian in R and non-zero at 0, then, for each r > 0 small enough, the restriction of the integral functional u → ∫ Ω f(u(x),∇u(x))dx to the sphere {u ∈ H(Ω) : ∫ Ω (|∇u(x)| + |u(x)|)dx = r} has a unique global minimum and a unique global maximum.

We introduce the notion of asymptotically almost nonexpansive curves which include almost-orbits of commutative semigroups of asymptotically nonexpansive type mappings and study the asymptotic behavior and prove nonlinear ergodic theorems for such curves. As applications of our main theorems, we obtain the results on the asymptotic behavior and ergodicity for a commutative semigroup of non-Lips...

The continuity of real functions is discussed. There is a function defined on some domain in real numbers which is continuous in a single point and on a subset of domain of the function. Main properties of real continuous functions are proved. Among them there is the Weierstraß Theorem. Algebraic features for real continuous functions are shown. Lipschitzian functions are introduced. The Lipsch...

We study continuous descent methods for the minimization of Lipschitzian functions defined on a general Banach space. We establish convergence theorems for those methods which are generated by approximate solutions to evolution equations governed by regular vector fields. Since the complement of the set of regular vector fields is σ-porous, we conclude that our results apply to most vector fiel...