Note on Generalization of Godunova-Levin-Opial Inequality

Abstract

Unauthenticated Download Date | 5/12/18 3:09 AM

On Opial’s Type Integral Inequalities

“…= ∏ n i=1 a n i −κ i i 2 ∏ n i=1 (n i − κ i ) 1/2 . From (18)- (20) and in view the elementary inequality (αβ) 1/2 ≤ 1 2 (α + β), α ≥ 0, β ≥ 0, we have a 1 0 · · · a n 0 ∂ κ 1 +···+κ n ∂s κ 1 1 · · · ∂s κ n n x 1 (s 1 , . .…”

On Opial-Type Integral Inequalities

“…(ii) Taking G = 1, (2.39) changes to a general form of the inequality which was given by Pečarić and Brnetić [19].…”

“…The inequality (1.1) has received considerable attention and a large number of papers dealing with new proofs, extensions, generalizations, variants, and discrete analogs of Opial's inequality have appeared in some literature [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. For an extensive survey on these inequalities, see [2,6].…”

Inequalities for Katugampola conformable partial derivatives

“…Opial's inequality and its generalizations, extensions, and discretizations play a fundamental role in establishing the existence and uniqueness of initial and boundary value problems for ordinary and partial differential equations as well as difference equations [2][3][4][5][6]. Inequality (1.1) has received considerable attention, and a large number of papers dealing with new proofs, extensions, generalizations, variants, and discrete analogues of Opial's inequality have appeared in the literature [7][8][9][10][11][12][13][14][15][16][17][18].…”