篇名 | Quasi-Mean Value Theorems for Symmetrically Differentiable Functions |
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卷期 | 27:3 |
作者 | Prasanna K. Sahoo |
頁次 | 279-301 |
關鍵字 | Auxiliary function 、 Darboux property 、 Flett’s mean value theorem 、 Lagrange mean value theorem 、 Lagrange mean value theorem of Cauchy like 、 Quasi-Flett mean value theorem 、 Quasi-Flett mean value theorem of Cauchy like 、 Quasi-Lagrange mean value theorem 、 Symmetric derivative |
出刊日期 | 201108 |
In this paper, we give a survey of results related the various quasimean value theorems for symmetrically differentiable functions and present some new results. The symmetric derivative of a real function is discussed and it’s elementary properties are pointed out. Some results leading to the quasi-Lagrange mean value theorem for the symmetrically differentiable functions are presented along with some generalizations.We also present several results concerning the quasi-Flett mean value theorem for the symmetrically differentiable functions. A new result that eliminate the boundary condition in the quasi-Flett mean theorem is also included. The quasi-Flett mean value theorem of Cauchy like is surveyed along with some related results. A new result that eliminate the boundary condition is presented related to the quasi-Flett mean value theorem of Cauchy like for the symmetrically differentiable functions.Further, by identifying several other new auxiliary functions,we present corresponding new quasi-mean value theorems which are variant of quasi-Lagrange mean value theorem, quasi-Flett mean value theorem, and quasi-Flett mean value theorem of Cauchy like for the symmetrically differentiable functions.