[PDF] Top 20 New Integral Inequalities in Quantum Calculus

... N.T., Integral inequalities of Gr¨ uss type via P´ olya-Szeg¨ o and Shisha-Mond results, East Asian Math.. R., Basic Hypergeometric Series , 2nd Edition, (2004), Encyclopedia of Mathemat[r] ... See full document

... a new class of preinvex functions which is called as generalized beta preinvex ...other new classes of preinvex functions. We derive some new integral inequalities using the approach of ... See full document

... Due to the rapid advancement of computing resource, there is a growing interest in developing parallel algorithms for the simulation of the Poisson–Schinequality problem. However, most approaches for Poisson–Sch ... See full document

... The applications of q-calculus play an important role in mathematics and the field of natu- ral sciences, such as physics and chemistry. It has many applications in orthogonal polyno- mials, number theory, and ... See full document

... fractional inequalities is now vast, and fractional inequalities are important in studying the existence, uniqueness, and other properties of fractional differential ...studied integral ... See full document

... In this paper, some of the most important integral inequalities of analysis are extended to quantum calculus. These include the Hölder, Hermite-Hadamard, trapezoid, Ostrowski, ... See full document

... Some new fractional integral inequalities are established by using the quantum Hahn integral for one and two functions bounded by quantum integrable ...fractional quantum ... See full document

... a new quantum integral identity with multiple pa- rameters, we have developed some quantum error estimations of different type inequal- ities through (α, m)-convexity, such as the midpoint-like ... See full document

... By introducing a parameter μ ∈ [0, 1], we established some quantum inequalities by means of the η-quasiconvexity. Our results sharpen, generalize, and extend some known results as can be seen in Remarks 17, ... See full document

... a new fractional integral, which generalizes the Riemann-Liouville and the Hadamard integrals into a single ...variational calculus applications, control theoretical applications, convexity and ... See full document

... In this paper we have established a new general Opial type integral inequality in q-calculus. Further, we investigated the Opial inequalities in q-calculus involving two functions and ... See full document

... The quantum calculus is known as the calculus without ...functions. Quantum difference operators have an interesting role due to their applications in several mathematical areas, such as ... See full document

... Quantum calculus has large applications in many mathematical areas such as number theory, special functions, quantum mechanics and mathematical ...a new quantum integral identity ... See full document

... Some new nonlinear integral inequalities of Gronwall type for retarded functions are established, which extend the results Lipovan 2003 and Pachpatte ...These inequalities can be used as basic ... See full document

... A q-analog, also called a q-extension or q-generalization is a mathematical expression parameterized by a quantity q that generalized a known expression and reduces to the known expression in the limit q  1  . There ... See full document

... The integral obtained is unified in nature and act as key formula from which we can obtain as their special cases, integral formulae concerning a large number of simpler special functions and ...also ... See full document

... 5.2. Definite Bigeometric Integral as a Limit of geometric Sum: So far G- integration has been defined as the inverse process of G-differentiation. But it is possible to regard a definite G-integral as the ... See full document

... and integral inequalities play a fundamental role in global existence,uniqueness, stability, and other properties of the solutions of various nonlinear differential equations; see ...and integral ... See full document

... 2000 Mathematics Subject Classification. Primary 39B62; Secondary 26D15. Key words and phrases. functional inequality, integral inequality, Jensen’s inequality. The second author was supported in part by NNSF ... See full document

... In the present paper, we investigate several distortion inequalities involving fractional calculus, Ruscheweyh derivative, and some well-known integral operators defined on the class Tδ,[r] ... See full document