Further nonlinear version of inequalities and their applications

Abstract

In this article, some new generalized nonlinear versions are established for integral and discrete analogues of inequalities, with advanced arguments that provide explicit bounds on unknown functions. The estimation given here can be used as a handy and powerful tool in the study of some classes of sum difference and integral equations. Some applications are also discussed here in order to illustrate the usefulness of our results.

Synchronization Analysis of Multiple Integral Inequalities Driven by Steklov Operator

“…Corollary 4. Assuming g, σ, ϕ, j, ρ, ψ 1 , y, and ψ 2 satisfies Theorem 1 and s(z 1 ) = ∞ in (15). Then, we have the following:…”

“…In view of their major significance and control throughout the long term, much exertion and time have been committed to the improvement and speculation of Hardy's and Copson's inequalities. However, these are not limited to the works in [5][6][7][8][9][10][11][12][13][14][15].…”

Some generalizations of the Hermite–Hadamard integral inequality

“…During 130 years of its existence, this inequality has been intensely studied, extended, and generalized by many authors. Some recent trends can be found in [5][6][7][8][9][10][11][12][13][14][15][16][17] and [18][19][20][21][22][23].…”

Derivation of dynamical integral inequalities based on two-dimensional time scales theory

“…Differential and integral inequalities have ended up being valuable instruments in investigating the differential and integral equations that are constructed by numerous analysts (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]). The analysis of the theory of time-scale dynamic equations, which goes back to its author Hilger [18], is a recent field of mathematics that has gained much interest.…”