scholarly journals Existence of solutions for a class of variational-hemivariational-like inequalities in Banach spaces

Filomat ◽  
2018 ◽  
Vol 32 (10) ◽  
pp. 3609-3622
Author(s):  
Lu-Chuan Ceng ◽  
Jen-Chih Yao ◽  
Yonghong Yao
Keyword(s):  
Banach Spaces ◽  
Existence Of Solutions ◽  
Directional Derivative ◽  
Existence Results ◽  
Solution Set ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Generalized Gradient ◽  
Reflexive Banach Spaces ◽  
Necessary And Sufficient

This paper is devoted to study the existence of solutions for a class of variational-hemivariationallike inequalities in reflexive Banach spaces. Using the notion of the stable (?,?)-quasimonotonicity, the properties of Clarke?s generalized directional derivative and Clarke?s generalized gradient, we establish some existence results of solutions when the constrained set is nonempty, bounded (or unbounded), closed and convex. Moreover, a sufficient condition to the boundedness of the solution set and a necessary and sufficient condition to the existence of solutions are also derived.

scholarly journals The Identification of Convex Function on Riemannian Manifold

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Li Zou ◽  
Xin Wen ◽  
Hamid Reza Karimi ◽  
Yan Shi
Keyword(s):  
Riemannian Manifold ◽  
Convex Function ◽  
Global Minimum ◽  
Directional Derivative ◽  
Inequality Constraints ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Generalized Gradient ◽  
Necessary And Sufficient ◽  
Global Minimum Point

The necessary and sufficient condition of convex function is significant in nonlinear convex programming. This paper presents the identification of convex function on Riemannian manifold by use of Penot generalized directional derivative and the Clarke generalized gradient. This paper also presents a method for judging whether a point is the global minimum point in the inequality constraints. Our objective here is to extend the content and proof the necessary and sufficient condition of convex function to Riemannian manifolds.

Orthogonal Fractional Factorial Plans

1980 ◽  
Vol 29 (3-4) ◽  
pp. 143-160 ◽  
Author(s):  
Rahul Mukerjee
Keyword(s):  
Broad Class ◽  
Existence Results ◽  
Fractional Factorial ◽  
The Other ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Equal Frequency ◽  
Other Hand ◽  
Necessary And Sufficient ◽  
Generally True

This paper shows that the criterion of proportional frequency for (unblocked) orthogonal fractional factorial plans, as suggested by some previous authors, is not generally true. On the other hand, the criterion of equal frequency has been established as a necessary and sufficient condition in the general case. Some other properties of orthogonal fractional factorial plans have been investigated. A necessary and sufficient condition for designs involving two or more blocks has also been presented. A broad class of non-existence results follow.

ON BI-BANACH FRAMES IN BANACH SPACES

2014 ◽  
Vol 12 (02) ◽  
pp. 1450015 ◽  
Author(s):  
SHALU SHARMA
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Banach Frames ◽  
Banach Frame ◽  
Necessary And Sufficient

Bi-Banach frames in Banach spaces have been defined and studied. A necessary and sufficient condition under which a Banach space has a Bi-Banach frame has been given. Finally, Pseudo exact retro Banach frames have been defined and studied.

scholarly journals Some results concerning frames in Banach spaces

2007 ◽  
Vol 38 (3) ◽  
pp. 267-276 ◽  
Author(s):  
S. K. Kaushik
Keyword(s):  
Finite Number ◽  
Banach Spaces ◽  
Necessary Condition ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Linearly Independent ◽  
Banach Frame ◽  
Minimal Sequence ◽  
Definition Of ◽  
Necessary And Sufficient

A necessary and sufficient condition for the associated sequence of functionals to a complete minimal sequence to be a Banach frame has been given. We give the definition of a weak-exact Banach frame, and observe that an exact Banach frame is weak-exact. An example of a weak-exact Banach frame which is not exact has been given. A necessary and sufficient condition for a Banach frame to be a weak-exact Banach frame has been obtained. Finally, a necessary condition for the perturbation of a retro Banach frame by a finite number of linearly independent vectors to be a retro Banach frame has been given.

ON FRAME SYSTEMS IN BANACH SPACES

2009 ◽  
Vol 07 (01) ◽  
pp. 1-7 ◽  
Author(s):  
P. K. JAIN ◽  
S. K. KAUSHIK ◽  
NISHA GUPTA
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Bessel Sequence ◽  
Banach Frame ◽  
Frame System ◽  
Frame Systems ◽  
Necessary And Sufficient

Banach frame systems in Banach spaces have been defined and studied. A sufficient condition under which a Banach space, having a Banach frame, has a Banach frame system has been given. Also, it has been proved that a Banach space E is separable if and only if E* has a Banach frame ({φn},T) with each φn weak*-continuous. Finally, a necessary and sufficient condition for a Banach Bessel sequence to be a Banach frame has been given.

On fusion frames in Banach spaces

2010 ◽  
Vol 18 (1) ◽  
pp. 121-130
Author(s):  
Shiv K. Kaushik ◽  
Varinder Kumar
Keyword(s):  
Banach Spaces ◽  
Complete Sequence ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Banach Frames ◽  
Fusion Frames ◽  
Banach Frame ◽  
Necessary And Sufficient

Abstract A necessary and sufficient condition for a complete sequence of subspaces to be a fusion Banach frame for E is given. Also, we introduce fusion Banach frame sequences and give a characterization for a complete sequence of subspaces of E to be a fusion Banach frame for E in terms of fusion Banach frame sequences. Finally, along with other results, we characterize fusion Banach frames in terms of Banach frames.

scholarly journals A further necessary and sufficient condition for strong convergence of nonlinear contraction semigroups and of iterative methods for accretive operators in Banach spaces

1995 ◽  
Vol 38 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Zong-Ben Xu ◽  
Yao-Lin Jiang ◽  
G. F. Roach
Keyword(s):  
Banach Space ◽  
Strong Convergence ◽  
Banach Spaces ◽  
Iterative Methods ◽  
Accretive Operator ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Accretive Operators ◽  
Uniformly Smooth ◽  
Necessary And Sufficient

Let A be a quasi-accretive operator defined in a uniformly smooth Banach space. We present a necessary and sufficient condition for the strong convergence of the semigroups generated by – A and of the steepest descent methods to a zero of A.

ON SOME CLASSES OF SCHAUDER FRAMES IN BANACH SPACES

2014 ◽  
Vol 12 (02) ◽  
pp. 1450022
Author(s):  
KHOLE TIMOTHY POUMAI
Keyword(s):  
Banach Spaces ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient ◽  
Schauder Frame

Various types of Schauder frames have been defined and studied. A necessary and sufficient condition for each type of Schauder frame is given. Finally, we give some theoretical applications of these types of Schauder frames.

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