Sentence examples for by applying some fixed from inspiring English sources

The problem is issued by applying some fixed point theorems and the properties of Green's function.

In this section, we show the existence of solutions for the problem (1.1) by applying some fixed point theorems.

By applying some fixed point theorems on cone, we gain a unique positive solution and construct two iterative sequences to approximate the solution.

Ahmad and Sivasundaram [14] studied a class of four-point nonlocal boundary value problem of nonlinear integrodifferential equations of fractional order by applying some fixed point theorems.

By applying some fixed point theorems in posets and by using the order-preserving property of mappings, we prove an existence theorem of extended Nash equilibriums for nonmonetized noncooperative games.

By applying some standard fixed point principles, some existence and uniqueness results are obtained.

In Section 4, by applying some standard fixed point principles, we verify the existence of solutions for problem (1.1 - 1.3 1.1 - 1.3

By applying some standard fixed point theorems, we obtain the sufficient conditions for the existence and uniqueness of solutions of the problem at hand.

By applying some standard fixed point theorems, Agarwal et al. [34] and Ahmad et al. [35] showed some existence results for sequential q-fractional integrodifferential equations with q-antiperiodic boundary conditions and nonlocal four-point boundary conditions, respectively.

We prove the existence and uniqueness of solutions for nonlinear integro-differential equations of fractional order with three-point nonlocal fractional boundary conditions by applying some standard fixed point theorems.

In a more recent work [49], the authors presented a novel idea of unification of anti-periodic and multipoint boundary conditions and developed the existence theory for sequential fractional differential equations by applying some standard fixed point theorems due to Banach, Krasnoselskii, Leray-Schauder alternative criterion, and Leray-Schauder degree theory.